Characteristic polynomials of connected graphs

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Polynomials

$G$

$\phi(G,x)$

comment: This is the complete graph $K_1$.

A_:

x^2 - 1

comment: This is the complete graph $K_2$.

BW:

x^3 - 2*x

comment: This is the path $P_3$.

Bw:

x^3 - 3*x - 2

comment: This is the complete graph $K_3$.

CF:

x^4 - 3*x^2

comment: This is the star $K_{1,3}$.

CL:

x^4 - 3*x^2 + 1

comment: This is the path $P_4$.

CN:

x^4 - 4*x^2 - 2*x + 1

C]:

x^4 - 4*x^2

comment: This is the cycle $C_4$.

C^:

x^4 - 5*x^2 - 4*x

comment: This is the diamond graph.

C~:

x^4 - 6*x^2 - 8*x - 3

comment: This is the complete graph $K_4$.

D?{:

x^5 - 4*x^3

comment: This is the star $K_{1,4}$.

D@s:

x^5 - 4*x^3 + 2*x

D@{:

x^5 - 5*x^3 - 2*x^2 + 2*x

DIk:

x^5 - 5*x^3 + 2*x

DBk:

x^5 - 5*x^3 - 2*x^2 + 3*x

comment: This is the bull graph.

DB{:

x^5 - 6*x^3 - 4*x^2 + 2*x

comment: This is the dart graph.

DFw:

x^5 - 6*x^3

comment: This is the complete bipartite graph $K_{2,3}$.

DF{:

x^5 - 7*x^3 - 6*x^2

DBg:

x^5 - 4*x^3 + 3*x

comment: This is the path $P_5$.

DK[:

x^5 - 5*x^3 - 2*x^2 + 4*x + 2

DK{:

x^5 - 6*x^3 - 4*x^2 + 5*x + 4

comment: This is the butterfly graph.

DLo:

x^5 - 5*x^3 + 5*x - 2

comment: This is the cycle $C_5$.

Dbk:

x^5 - 6*x^3 - 2*x^2 + 4*x

comment: This is the house graph.

DL{:

x^5 - 7*x^3 - 6*x^2 + 3*x + 2

DJk:

x^5 - 6*x^3 - 4*x^2 + 3*x + 2

DJ{:

x^5 - 7*x^3 - 8*x^2 + 2

DN{:

x^5 - 8*x^3 - 10*x^2 - x + 2

comment: This is the house X graph.

DNw:

x^5 - 7*x^3 - 4*x^2 + 2*x

D]{:

x^5 - 8*x^3 - 8*x^2

comment: This is the wheel $W_5$.

D^{:

x^5 - 9*x^3 - 14*x^2 - 6*x

D~{:

x^5 - 10*x^3 - 20*x^2 - 15*x - 4

comment: This is the complete graph $K_5$.

E?Bw:

x^6 - 5*x^4

comment: This is the star $K_{1,5}$.

E?Fg:

x^6 - 5*x^4 + 3*x^2

E?Fw:

x^6 - 6*x^4 - 2*x^3 + 3*x^2

E@FG:

x^6 - 5*x^4 + 5*x^2

E?NG:

x^6 - 5*x^4 + 4*x^2

E@JW:

x^6 - 6*x^4 + 4*x^2

E?NW:

x^6 - 6*x^4 - 2*x^3 + 5*x^2

E?Nw:

x^6 - 7*x^4 - 4*x^3 + 4*x^2

E?]o:

x^6 - 6*x^4 + 5*x^2

E?^o:

x^6 - 7*x^4 + 3*x^2

E?]w:

x^6 - 7*x^4 - 4*x^3 + 5*x^2

E?^w:

x^6 - 8*x^4 - 6*x^3 + 3*x^2

E?~o:

x^6 - 8*x^4

comment: This is the complete bipartite graph $K_{2,4}$.

E?~w:

x^6 - 9*x^4 - 8*x^3

E@QW:

x^6 - 5*x^4 + 5*x^2 - 1

E@`w:

x^6 - 6*x^4 - 2*x^3 + 6*x^2 + 2*x - 1

E@Rw:

x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x - 1

comment: It has the same characteristic polynomial as E@]o.

E@YW:

x^6 - 6*x^4 + 5*x^2 - 1

EHQW:

x^6 - 6*x^4 + 8*x^2 - 2*x - 1

E@UW:

x^6 - 6*x^4 - 2*x^3 + 6*x^2 - 1

EGNW:

x^6 - 7*x^4 - 2*x^3 + 7*x^2 - 1

EAMw:

x^6 - 7*x^4 - 4*x^3 + 6*x^2 + 2*x - 1

E@Vw:

x^6 - 8*x^4 - 6*x^3 + 6*x^2 + 2*x - 1

E@YO:

x^6 - 5*x^4 + 6*x^2 - 1

comment: This is the path $P_6$.

EI_w:

x^6 - 6*x^4 + 6*x^2

EGdo:

x^6 - 6*x^4 - 2*x^3 + 8*x^2 + 4*x - 1

EGcw:

x^6 - 6*x^4 - 2*x^3 + 7*x^2 + 2*x - 1

E@ow:

x^6 - 6*x^4 - 2*x^3 + 7*x^2 + 4*x

EK`w:

x^6 - 7*x^4 - 2*x^3 + 8*x^2 + 4*x

ECXw:

x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x

EGdw:

x^6 - 7*x^4 - 4*x^3 + 9*x^2 + 6*x - 1

E_Nw:

x^6 - 8*x^4 - 6*x^3 + 9*x^2 + 8*x

E@NW:

x^6 - 7*x^4 - 4*x^3 + 6*x^2 + 4*x

E@Nw:

x^6 - 8*x^4 - 8*x^3 + 3*x^2 + 4*x

E_]o:

x^6 - 7*x^4 + 9*x^2 - 4*x

EENg:

x^6 - 8*x^4 - 2*x^3 + 7*x^2

EC\w:

x^6 - 8*x^4 - 6*x^3 + 5*x^2 + 4*x

E@^W:

x^6 - 8*x^4 - 6*x^3 + 7*x^2 + 4*x - 1

E_]w:

x^6 - 8*x^4 - 4*x^3 + 8*x^2

E@vw:

x^6 - 9*x^4 - 8*x^3 + 6*x^2 + 4*x

E@^o:

x^6 - 8*x^4 - 4*x^3 + 6*x^2 + 2*x - 1

E@]w:

x^6 - 8*x^4 - 8*x^3 + 4*x^2 + 4*x - 1

E@^w:

x^6 - 9*x^4 - 10*x^3 + 3*x^2 + 4*x - 1

E@~o:

x^6 - 9*x^4 - 4*x^3 + 4*x^2

E@~w:

x^6 - 10*x^4 - 12*x^3 + x^2 + 4*x

EBYW:

x^6 - 7*x^4 + 4*x^2

EBYw:

x^6 - 8*x^4 - 4*x^3 + 6*x^2

EBZw:

x^6 - 9*x^4 - 8*x^3 + 4*x^2

EIe_:

x^6 - 6*x^4 + 9*x^2 - 4

comment: This is the cycle $C_6$.

EKNG:

x^6 - 7*x^4 + 7*x^2 - 1

EHUW:

x^6 - 7*x^4 - 2*x^3 + 8*x^2

EoLW:

x^6 - 7*x^4 - 2*x^3 + 11*x^2 + 2*x - 4

E@]o:

x^6 - 7*x^4 - 4*x^3 + 7*x^2 + 4*x - 1

comment: It has the same characteristic polynomial as E@Rw.

EA]o:

x^6 - 7*x^4 - 2*x^3 + 8*x^2 + 2*x - 1

EaMw:

x^6 - 8*x^4 - 4*x^3 + 9*x^2 + 4*x - 1

EBhw:

x^6 - 8*x^4 - 6*x^3 + 8*x^2 + 6*x

EBjW:

x^6 - 8*x^4 - 4*x^3 + 11*x^2 + 4*x - 4

EBjw:

x^6 - 9*x^4 - 8*x^3 + 9*x^2 + 8*x - 1

EImo:

x^6 - 8*x^4 + 4*x^2

EJYW:

x^6 - 8*x^4 - 4*x^3 + 7*x^2 + 4*x

EIno:

x^6 - 9*x^4 - 4*x^3 + 7*x^2

EImw:

x^6 - 9*x^4 - 6*x^3 + 6*x^2 + 4*x

EInw:

x^6 - 10*x^4 - 10*x^3 + 5*x^2 + 4*x

EI]w:

x^6 - 9*x^4 - 8*x^3 + 5*x^2 + 4*x

EB]w:

x^6 - 9*x^4 - 10*x^3 + 4*x^2 + 6*x

EB^w:

x^6 - 10*x^4 - 14*x^3 - x^2 + 4*x

EHuw:

x^6 - 9*x^4 - 6*x^3 + 8*x^2 + 2*x - 1

EBnW:

x^6 - 9*x^4 - 8*x^3 + 9*x^2 + 6*x - 4

EBnw:

x^6 - 10*x^4 - 12*x^3 + 4*x^2 + 6*x - 1

EB~w:

x^6 - 11*x^4 - 16*x^3 - 2*x^2 + 4*x

EFz_:

x^6 - 9*x^4

comment: This is the complete bipartite graph $K_{3,3}$.

Es\w:

x^6 - 10*x^4 - 6*x^3 + 3*x^2

EB~o:

x^6 - 10*x^4 - 8*x^3 + 4*x^2

EFzw:

x^6 - 11*x^4 - 12*x^3

EF~w:

x^6 - 12*x^4 - 20*x^3 - 9*x^2

EPTW:

x^6 - 7*x^4 - 4*x^3 + 8*x^2 + 6*x

E`NG:

x^6 - 7*x^4 - 4*x^3 + 11*x^2 + 12*x + 3

E`NW:

x^6 - 8*x^4 - 6*x^3 + 11*x^2 + 14*x + 4

E`Lw:

x^6 - 8*x^4 - 8*x^3 + 6*x^2 + 10*x + 3

E`Nw:

x^6 - 9*x^4 - 10*x^3 + 9*x^2 + 18*x + 7

EJeg:

x^6 - 8*x^4 - 4*x^3 + 12*x^2 + 8*x

EJqw:

x^6 - 9*x^4 - 6*x^3 + 11*x^2 + 8*x - 1

EK\w:

x^6 - 9*x^4 - 10*x^3 + 5*x^2 + 10*x + 3

EK]w:

x^6 - 9*x^4 - 8*x^3 + 10*x^2 + 12*x + 3

E`]w:

x^6 - 9*x^4 - 8*x^3 + 8*x^2 + 8*x

EK^w:

x^6 - 10*x^4 - 12*x^3 + 7*x^2 + 14*x + 4

EK~o:

x^6 - 10*x^4 - 8*x^3 + 9*x^2 + 8*x

EK~w:

x^6 - 11*x^4 - 16*x^3 + 3*x^2 + 16*x + 7

EBn_:

x^6 - 8*x^4 - 2*x^3 + 10*x^2 - 2*x - 1

E`]o:

x^6 - 8*x^4 - 4*x^3 + 12*x^2 + 4*x - 5

ELpw:

x^6 - 9*x^4 - 6*x^3 + 11*x^2 + 4*x - 4

ELrw:

x^6 - 10*x^4 - 10*x^3 + 10*x^2 + 8*x - 5

comment: This is the wheel $W_6$.

ELv_:

x^6 - 9*x^4 - 4*x^3 + 12*x^2

Ek]w:

x^6 - 10*x^4 - 8*x^3 + 9*x^2 + 4*x - 1

EJnW:

x^6 - 10*x^4 - 10*x^3 + 8*x^2 + 8*x

Ebnw:

x^6 - 11*x^4 - 14*x^3 + 4*x^2 + 8*x

EL~w:

x^6 - 12*x^4 - 20*x^3 - 4*x^2 + 8*x + 3

ER^W:

x^6 - 10*x^4 - 10*x^3 + 6*x^2 + 6*x - 1

EJmw:

x^6 - 10*x^4 - 12*x^3 + 5*x^2 + 12*x + 4

EJnw:

x^6 - 11*x^4 - 16*x^3 + x^2 + 10*x + 3

EJ]w:

x^6 - 10*x^4 - 14*x^3 + 8*x + 3

EJ^w:

x^6 - 11*x^4 - 20*x^3 - 9*x^2 + 4*x + 3

EJ~w:

x^6 - 12*x^4 - 22*x^3 - 9*x^2 + 6*x + 4

EN~w:

x^6 - 13*x^4 - 26*x^3 - 15*x^2 + 2*x + 3

EL~o:

x^6 - 11*x^4 - 12*x^3 + 5*x^2 + 4*x

EJ~o:

x^6 - 11*x^4 - 14*x^3 + 4*x

Ejmw:

x^6 - 11*x^4 - 12*x^3 + 3*x^2 + 4*x - 1

ENzw:

x^6 - 12*x^4 - 18*x^3 - 3*x^2 + 4*x

E]~o:

x^6 - 12*x^4 - 16*x^3

E]~w:

x^6 - 13*x^4 - 24*x^3 - 12*x^2

E^~w:

x^6 - 14*x^4 - 32*x^3 - 27*x^2 - 8*x

E~~w:

x^6 - 15*x^4 - 40*x^3 - 45*x^2 - 24*x - 5

comment: This is the complete graph $K_6$.

F??Fw:

x^7 - 6*x^5

comment: This is the star $K_{1,6}$.

F??Ng:

x^7 - 6*x^5 + 4*x^3

F??Nw:

x^7 - 7*x^5 - 2*x^4 + 4*x^3

F?CNG:

x^7 - 6*x^5 + 7*x^3

F??^G:

x^7 - 6*x^5 + 6*x^3

F??^o:

x^7 - 7*x^5 + 6*x^3

F??^W:

x^7 - 7*x^5 - 2*x^4 + 7*x^3

F??^w:

x^7 - 8*x^5 - 4*x^4 + 6*x^3

F??}O:

x^7 - 6*x^5 + 8*x^3

F??}o:

x^7 - 7*x^5 + 8*x^3

F??}W:

x^7 - 7*x^5 - 2*x^4 + 8*x^3

F??~o:

x^7 - 8*x^5 + 6*x^3

F??}w:

x^7 - 8*x^5 - 4*x^4 + 8*x^3

F??~w:

x^7 - 9*x^5 - 6*x^4 + 6*x^3

F?@|o:

x^7 - 8*x^5 + 7*x^3

F?@~o:

x^7 - 9*x^5 + 4*x^3

F?@|w:

x^7 - 9*x^5 - 6*x^4 + 7*x^3

F?@~w:

x^7 - 10*x^5 - 8*x^4 + 4*x^3

F?B~o:

x^7 - 10*x^5

comment: This is the complete bipartite graph $K_{2,5}$.

F?B~w:

x^7 - 11*x^5 - 10*x^4

F?CeW:

x^7 - 6*x^5 + 7*x^3 - 2*x

F@?Mw:

x^7 - 7*x^5 - 2*x^4 + 8*x^3 + 2*x^2 - 2*x

F?Cfw:

x^7 - 8*x^5 - 4*x^4 + 9*x^3 + 4*x^2 - 2*x

F@?]O:

x^7 - 6*x^5 + 9*x^3 - 2*x

F?Cmg:

x^7 - 7*x^5 + 8*x^3 - 2*x

F@?]W:

x^7 - 7*x^5 - 2*x^4 + 10*x^3 + 2*x^2 - 2*x

F@CeW:

x^7 - 7*x^5 + 11*x^3 - 2*x^2 - 2*x

F?CmW:

x^7 - 7*x^5 - 2*x^4 + 9*x^3 - 2*x

F@?^W:

x^7 - 8*x^5 - 2*x^4 + 10*x^3 - 2*x

F?G]w:

x^7 - 8*x^5 - 4*x^4 + 9*x^3 + 2*x^2 - 2*x

F?Cnw:

x^7 - 9*x^5 - 6*x^4 + 9*x^3 + 2*x^2 - 2*x

F@OKg:

x^7 - 6*x^5 + 9*x^3 - 3*x

F?DcW:

x^7 - 6*x^5 + 8*x^3 - 2*x

F@IAw:

x^7 - 7*x^5 + 9*x^3 - 2*x

F@AJo:

x^7 - 7*x^5 - 2*x^4 + 11*x^3 + 4*x^2 - 3*x

F@@Kw:

x^7 - 7*x^5 - 2*x^4 + 10*x^3 + 2*x^2 - 3*x

F?Dcw:

x^7 - 7*x^5 - 2*x^4 + 10*x^3 + 4*x^2 - 2*x

F@PDw:

x^7 - 8*x^5 - 2*x^4 + 11*x^3 + 4*x^2 - 2*x

F?_rw:

x^7 - 8*x^5 - 4*x^4 + 10*x^3 + 4*x^2 - 2*x

comment: It has the same characteristic polynomial as F?Dkw.

F@@Lw:

x^7 - 8*x^5 - 4*x^4 + 12*x^3 + 6*x^2 - 3*x

comment: It has the same characteristic polynomial as FGG[w.

FG?^w:

x^7 - 9*x^5 - 6*x^4 + 12*x^3 + 8*x^2 - 2*x

F?C^G:

x^7 - 7*x^5 - 2*x^4 + 10*x^3 + 6*x^2

F?C^W:

x^7 - 8*x^5 - 4*x^4 + 9*x^3 + 6*x^2

F?C^w:

x^7 - 9*x^5 - 8*x^4 + 6*x^3 + 6*x^2

F@@ko:

x^7 - 7*x^5 + 12*x^3 - 2*x^2 - 3*x

F?O|o:

x^7 - 8*x^5 + 8*x^3 - 2*x

F?W\g:

x^7 - 8*x^5 - 2*x^4 + 12*x^3 + 2*x^2 - 3*x

FG?}o:

x^7 - 8*x^5 + 13*x^3 - 4*x^2 - 2*x

F?H[w:

x^7 - 8*x^5 - 4*x^4 + 10*x^3 + 2*x^2 - 3*x

F?Dkw:

x^7 - 8*x^5 - 4*x^4 + 10*x^3 + 4*x^2 - 2*x

comment: It has the same characteristic polynomial as F?_rw.

F@@kw:

x^7 - 8*x^5 - 2*x^4 + 11*x^3 - 3*x

F?W^g:

x^7 - 9*x^5 - 2*x^4 + 11*x^3 - 2*x

F?O|w:

x^7 - 9*x^5 - 6*x^4 + 9*x^3 + 4*x^2 - 2*x

F?Dlw:

x^7 - 9*x^5 - 6*x^4 + 11*x^3 + 4*x^2 - 3*x

FG?}w:

x^7 - 9*x^5 - 4*x^4 + 12*x^3 - 2*x

F?Dnw:

x^7 - 10*x^5 - 8*x^4 + 10*x^3 + 4*x^2 - 2*x

comment: It has the same characteristic polynomial as F@H\w.

F?O|_:

x^7 - 7*x^5 + 10*x^3 - 2*x

F@?}O:

x^7 - 7*x^5 - 2*x^4 + 12*x^3 + 6*x^2 - 2*x

F?`ro:

x^7 - 8*x^5 + 9*x^3

FGAZo:

x^7 - 8*x^5 - 2*x^4 + 13*x^3 + 6*x^2 - 2*x

F?O|g:

x^7 - 8*x^5 - 4*x^4 + 11*x^3 + 4*x^2 - 2*x

F@?}W:

x^7 - 8*x^5 - 4*x^4 + 13*x^3 + 8*x^2 - 2*x

comment: It has the same characteristic polynomial as F?org.

F_?~o:

x^7 - 9*x^5 - 2*x^4 + 12*x^3 + 6*x^2

F?`rw:

x^7 - 9*x^5 - 6*x^4 + 10*x^3 + 6*x^2

FGAZw:

x^7 - 9*x^5 - 6*x^4 + 14*x^3 + 10*x^2 - 2*x

F_?~w:

x^7 - 10*x^5 - 8*x^4 + 13*x^3 + 12*x^2

comment: It has the same characteristic polynomial as FGyw`.

F?C~O:

x^7 - 8*x^5 - 2*x^4 + 12*x^3 + 4*x^2 - 2*x

F@C]W:

x^7 - 8*x^5 - 4*x^4 + 11*x^3 + 6*x^2 - 2*x

F?C~o:

x^7 - 9*x^5 - 4*x^4 + 10*x^3 + 4*x^2 - 2*x

F?C~W:

x^7 - 9*x^5 - 6*x^4 + 11*x^3 + 6*x^2 - 2*x

F?C}w:

x^7 - 9*x^5 - 8*x^4 + 8*x^3 + 6*x^2 - 2*x

F?C~w:

x^7 - 10*x^5 - 10*x^4 + 7*x^3 + 6*x^2 - 2*x

F?`zo:

x^7 - 9*x^5 + 6*x^3

F?D~O:

x^7 - 9*x^5 - 2*x^4 + 12*x^3 + 2*x^2 - 2*x

F_@|o:

x^7 - 9*x^5 + 13*x^3 - 6*x^2

F?Fno:

x^7 - 10*x^5 - 2*x^4 + 10*x^3

F?`zw:

x^7 - 10*x^5 - 8*x^4 + 7*x^3 + 6*x^2

F?D~W:

x^7 - 10*x^5 - 8*x^4 + 11*x^3 + 6*x^2 - 2*x

F_@|w:

x^7 - 10*x^5 - 6*x^4 + 12*x^3

F?Fnw:

x^7 - 11*x^5 - 10*x^4 + 9*x^3 + 6*x^2

F?D|o:

x^7 - 9*x^5 - 4*x^4 + 11*x^3 + 4*x^2 - 3*x

F?D~o:

x^7 - 10*x^5 - 4*x^4 + 9*x^3 + 2*x^2 - 2*x

F?D|w:

x^7 - 10*x^5 - 10*x^4 + 8*x^3 + 6*x^2 - 3*x

F?D~w:

x^7 - 11*x^5 - 12*x^4 + 6*x^3 + 6*x^2 - 2*x

F?F~o:

x^7 - 11*x^5 - 4*x^4 + 6*x^3

F?F~w:

x^7 - 12*x^5 - 14*x^4 + 3*x^3 + 6*x^2

F?KuW:

x^7 - 8*x^5 + 8*x^3

F@CmW:

x^7 - 8*x^5 - 2*x^4 + 12*x^3

F?Kuw:

x^7 - 9*x^5 - 4*x^4 + 10*x^3

F?Kvw:

x^7 - 10*x^5 - 8*x^4 + 8*x^3

FICcW:

x^7 - 7*x^5 + 13*x^3 - 7*x

F@HSW:

x^7 - 7*x^5 + 12*x^3 - 2*x^2 - 4*x

F?_yo:

x^7 - 7*x^5 + 9*x^3 - 3*x

F@O^G:

x^7 - 8*x^5 + 11*x^3 - 4*x

FGG[w:

x^7 - 8*x^5 - 4*x^4 + 12*x^3 + 6*x^2 - 3*x

comment: It has the same characteristic polynomial as F@@Lw.

F@Okw:

x^7 - 8*x^5 - 2*x^4 + 12*x^3 - 3*x

FI?\W:

x^7 - 8*x^5 - 2*x^4 + 15*x^3 + 2*x^2 - 7*x

F@O[w:

x^7 - 8*x^5 - 4*x^4 + 11*x^3 + 4*x^2 - 4*x

F?StW:

x^7 - 8*x^5 - 2*x^4 + 12*x^3 + 2*x^2 - 4*x

FGG]w:

x^7 - 9*x^5 - 4*x^4 + 13*x^3 + 4*x^2 - 4*x

F?MRw:

x^7 - 9*x^5 - 6*x^4 + 12*x^3 + 6*x^2 - 3*x

F?LVW:

x^7 - 9*x^5 - 4*x^4 + 15*x^3 + 4*x^2 - 7*x

F?LVw:

x^7 - 10*x^5 - 8*x^4 + 13*x^3 + 8*x^2 - 4*x

FIAHo:

x^7 - 7*x^5 + 11*x^3 - 2*x

F?StG:

x^7 - 7*x^5 - 2*x^4 + 12*x^3 + 4*x^2 - 4*x

F@G]G:

x^7 - 7*x^5 + 10*x^3

F?oow:

x^7 - 7*x^5 - 2*x^4 + 11*x^3 + 4*x^2 - 2*x

FIa@w:

x^7 - 8*x^5 + 12*x^3

F?org:

x^7 - 8*x^5 - 4*x^4 + 13*x^3 + 8*x^2 - 2*x

comment: It has the same characteristic polynomial as F@?}W.

FIAHw:

x^7 - 8*x^5 - 2*x^4 + 13*x^3 + 4*x^2 - 2*x

F?opw:

x^7 - 8*x^5 - 4*x^4 + 12*x^3 + 8*x^2

F?YPw:

x^7 - 8*x^5 - 4*x^4 + 14*x^3 + 8*x^2 - 4*x

Fo?Zw:

x^7 - 9*x^5 - 4*x^4 + 14*x^3 + 8*x^2

F?NBw:

x^7 - 9*x^5 - 6*x^4 + 15*x^3 + 12*x^2 - 2*x

F?NFw:

x^7 - 10*x^5 - 8*x^4 + 16*x^3 + 16*x^2

F@H[o:

x^7 - 8*x^5 + 9*x^3 - 2*x

F@TTW:

x^7 - 9*x^5 + 9*x^3 - 2*x

F@IZo:

x^7 - 9*x^5 - 4*x^4 + 12*x^3 + 4*x^2 - 2*x

F?Tto:

x^7 - 9*x^5 - 2*x^4 + 15*x^3 - 2*x^2 - 3*x

F@H[w:

x^7 - 9*x^5 - 4*x^4 + 11*x^3 - 2*x

F@H^o:

x^7 - 10*x^5 - 4*x^4 + 12*x^3 - 2*x

F@H]w:

x^7 - 10*x^5 - 6*x^4 + 11*x^3 + 4*x^2 - 2*x

F@H\w:

x^7 - 10*x^5 - 8*x^4 + 10*x^3 + 4*x^2 - 2*x

comment: It has the same characteristic polynomial as F?Dnw.

F@Dmw:

x^7 - 10*x^5 - 6*x^4 + 13*x^3 + 2*x^2 - 3*x

F@H^w:

x^7 - 11*x^5 - 10*x^4 + 10*x^3 + 4*x^2 - 2*x

Fo?yo:

x^7 - 8*x^5 + 15*x^3 - 8*x

F?L^?:

x^7 - 8*x^5 - 2*x^4 + 16*x^3 + 4*x^2 - 7*x

comment: It has the same characteristic polynomial as FQ@w`.

F?[uG:

x^7 - 8*x^5 + 14*x^3 - 4*x^2 - 2*x

F_LLg:

x^7 - 9*x^5 + 12*x^3 - 2*x

F?Uro:

x^7 - 9*x^5 - 4*x^4 + 15*x^3 + 8*x^2 - 3*x

F?]Rg:

x^7 - 9*x^5 - 2*x^4 + 13*x^3

F?svG:

x^7 - 9*x^5 - 2*x^4 + 18*x^3 + 2*x^2 - 8*x

FADlW:

x^7 - 9*x^5 - 4*x^4 + 14*x^3 + 4*x^2 - 3*x

FCDjW:

x^7 - 9*x^5 - 6*x^4 + 12*x^3 + 10*x^2

Fo?yw:

x^7 - 9*x^5 - 4*x^4 + 17*x^3 + 6*x^2 - 8*x

comment: It has the same characteristic polynomial as FAYPw.

F?NPw:

x^7 - 9*x^5 - 6*x^4 + 13*x^3 + 10*x^2

FEG^W:

x^7 - 10*x^5 - 4*x^4 + 15*x^3 + 6*x^2 - 2*x

FCDnW:

x^7 - 10*x^5 - 6*x^4 + 14*x^3 + 8*x^2 - 2*x

F@FJw:

x^7 - 10*x^5 - 8*x^4 + 15*x^3 + 12*x^2 - 3*x

F?drw:

x^7 - 10*x^5 - 8*x^4 + 13*x^3 + 10*x^2

F?NVW:

x^7 - 10*x^5 - 6*x^4 + 18*x^3 + 8*x^2 - 8*x

F@FNw:

x^7 - 11*x^5 - 10*x^4 + 15*x^3 + 14*x^2 - 2*x

F@KuW:

x^7 - 9*x^5 - 4*x^4 + 12*x^3 + 8*x^2

F@G}w:

x^7 - 10*x^5 - 8*x^4 + 10*x^3 + 8*x^2

F?K}w:

x^7 - 10*x^5 - 10*x^4 + 9*x^3 + 10*x^2

F?K~w:

x^7 - 11*x^5 - 14*x^4 + 4*x^3 + 8*x^2

F?L^_:

x^7 - 9*x^5 - 2*x^4 + 15*x^3 - 4*x

FAEhw:

x^7 - 9*x^5 - 6*x^4 + 13*x^3 + 8*x^2 - 3*x

F?L\g:

x^7 - 9*x^5 - 4*x^4 + 11*x^3 + 2*x^2 - 3*x

F?L^G:

x^7 - 9*x^5 - 4*x^4 + 16*x^3 + 6*x^2 - 7*x

F?L[w:

x^7 - 9*x^5 - 8*x^4 + 9*x^3 + 6*x^2 - 4*x

F@D^W:

x^7 - 10*x^5 - 6*x^4 + 13*x^3 + 4*x^2 - 4*x

F?S|w:

x^7 - 10*x^5 - 10*x^4 + 9*x^3 + 8*x^2 - 3*x

F?L^W:

x^7 - 10*x^5 - 8*x^4 + 14*x^3 + 8*x^2 - 7*x

F?L^w:

x^7 - 11*x^5 - 12*x^4 + 9*x^3 + 8*x^2 - 4*x

F?NN_:

x^7 - 9*x^5 + 16*x^3 - 8*x^2

F?drW:

x^7 - 9*x^5 - 4*x^4 + 14*x^3 + 4*x^2 - 2*x

F?LuW:

x^7 - 9*x^5 - 2*x^4 + 12*x^3 - 2*x

F?K}W:

x^7 - 9*x^5 - 6*x^4 + 10*x^3 + 8*x^2

F?Lkw:

x^7 - 9*x^5 - 6*x^4 + 12*x^3 + 6*x^2 - 4*x

F?NNg:

x^7 - 10*x^5 - 4*x^4 + 14*x^3

F?NJw:

x^7 - 10*x^5 - 8*x^4 + 12*x^3 + 8*x^2 - 2*x

F?NNw:

x^7 - 11*x^5 - 10*x^4 + 12*x^3 + 8*x^2

F@J]o:

x^7 - 10*x^5 + 8*x^3

F@J^o:

x^7 - 11*x^5 - 4*x^4 + 12*x^3

F@J]w:

x^7 - 11*x^5 - 8*x^4 + 10*x^3 + 8*x^2

F@J^w:

x^7 - 12*x^5 - 12*x^4 + 10*x^3 + 8*x^2

F@H}o:

x^7 - 10*x^5 - 4*x^4 + 13*x^3 + 4*x^2 - 2*x

F?L~o:

x^7 - 11*x^5 - 8*x^4 + 10*x^3 + 4*x^2 - 2*x

F@H}w:

x^7 - 11*x^5 - 10*x^4 + 11*x^3 + 8*x^2 - 2*x

F?L|w:

x^7 - 11*x^5 - 14*x^4 + 5*x^3 + 8*x^2 - 2*x

F?L~w:

x^7 - 12*x^5 - 16*x^4 + 4*x^3 + 8*x^2 - 2*x

F@Fmo:

x^7 - 10*x^5 - 2*x^4 + 16*x^3 - 4*x^2 - 2*x

F?s~g:

x^7 - 11*x^5 - 6*x^4 + 13*x^3 + 2*x^2 - 2*x

F@Fmw:

x^7 - 11*x^5 - 8*x^4 + 14*x^3 + 4*x^2 - 2*x

F?L}w:

x^7 - 11*x^5 - 12*x^4 + 10*x^3 + 10*x^2 - 3*x

F?dzw:

x^7 - 11*x^5 - 12*x^4 + 8*x^3 + 10*x^2

F?N^W:

x^7 - 11*x^5 - 10*x^4 + 15*x^3 + 10*x^2 - 8*x

F?N^w:

x^7 - 12*x^5 - 14*x^4 + 9*x^3 + 10*x^2 - 2*x

F?N~o:

x^7 - 12*x^5 - 8*x^4 + 8*x^3

F?N~w:

x^7 - 13*x^5 - 18*x^4 + 2*x^3 + 8*x^2

FBXcw:

x^7 - 10*x^5 + 6*x^3

F?\sw:

x^7 - 10*x^5 - 4*x^4 + 10*x^3

FIO|w:

x^7 - 11*x^5 - 6*x^4 + 9*x^3

F?\tw:

x^7 - 11*x^5 - 8*x^4 + 10*x^3

F?\vw:

x^7 - 12*x^5 - 12*x^4 + 6*x^3

F?]v_:

x^7 - 10*x^5 + 11*x^3 - 2*x

F?lrg:

x^7 - 10*x^5 - 6*x^4 + 13*x^3 + 10*x^2

F?\tg:

x^7 - 10*x^5 - 4*x^4 + 13*x^3

FBEmW:

x^7 - 10*x^5 - 4*x^4 + 18*x^3 + 4*x^2 - 7*x

F?L|o:

x^7 - 10*x^5 - 8*x^4 + 11*x^3 + 8*x^2 - 2*x

F?T|o:

x^7 - 10*x^5 - 6*x^4 + 14*x^3 + 6*x^2 - 3*x

F?v`w:

x^7 - 10*x^5 - 4*x^4 + 17*x^3 + 4*x^2 - 8*x

comment: It has the same characteristic polynomial as FA_~o.

F?lvg:

x^7 - 11*x^5 - 6*x^4 + 14*x^3 + 6*x^2 - 2*x

F?]rw:

x^7 - 11*x^5 - 10*x^4 + 12*x^3 + 10*x^2

F?]uw:

x^7 - 11*x^5 - 8*x^4 + 17*x^3 + 8*x^2 - 7*x

F?]vw:

x^7 - 12*x^5 - 12*x^4 + 13*x^3 + 12*x^2 - 2*x

FIQ|o:

x^7 - 11*x^5 + 6*x^3

F?\~_:

x^7 - 11*x^5 - 6*x^4 + 10*x^3 + 6*x^2

F?]~_:

x^7 - 11*x^5 - 4*x^4 + 15*x^3 - 2*x^2 - 2*x

F?^vo:

x^7 - 12*x^5 - 6*x^4 + 10*x^3

FIQ|w:

x^7 - 12*x^5 - 8*x^4 + 9*x^3 + 6*x^2

F?^vw:

x^7 - 13*x^5 - 14*x^4 + 7*x^3 + 6*x^2

F?\~g:

x^7 - 12*x^5 - 12*x^4 + 7*x^3 + 6*x^2

F?\|w:

x^7 - 12*x^5 - 16*x^4 + 5*x^3 + 10*x^2

F?\~w:

x^7 - 13*x^5 - 20*x^4 - 2*x^3 + 6*x^2

F?^tw:

x^7 - 12*x^5 - 10*x^4 + 12*x^3 + 4*x^2 - 2*x

F?]}w:

x^7 - 12*x^5 - 14*x^4 + 12*x^3 + 12*x^2 - 7*x

comment: It has the same characteristic polynomial as F@U^w.

F?]~w:

x^7 - 13*x^5 - 18*x^4 + 5*x^3 + 10*x^2 - 2*x

F?^~w:

x^7 - 14*x^5 - 22*x^4 - 3*x^3 + 6*x^2

F?~v_:

x^7 - 12*x^5

comment: This is the complete bipartite graph $K_{3,4}$.

F?~vg:

x^7 - 13*x^5 - 8*x^4 + 4*x^3

F?^~o:

x^7 - 13*x^5 - 12*x^4 + 6*x^3

F?~vw:

x^7 - 14*x^5 - 16*x^4

F?~~w:

x^7 - 15*x^5 - 26*x^4 - 12*x^3

F@Q?w:

x^7 - 6*x^5 + 9*x^3 - 4*x

F@Q@w:

x^7 - 7*x^5 - 2*x^4 + 11*x^3 + 4*x^2 - 5*x - 2

F@QBw:

x^7 - 8*x^5 - 4*x^4 + 13*x^3 + 8*x^2 - 6*x - 4

F@QFw:

x^7 - 9*x^5 - 6*x^4 + 15*x^3 + 12*x^2 - 7*x - 6

F@HSO:

x^7 - 6*x^5 + 10*x^3 - 4*x

comment: This is the path $P_7$.

F@O\G:

x^7 - 7*x^5 + 10*x^3 - 3*x

FA_pW:

x^7 - 7*x^5 - 2*x^4 + 12*x^3 + 4*x^2 - 5*x - 2

FHQ?w:

x^7 - 7*x^5 + 13*x^3 - 2*x^2 - 6*x + 2

F@OsW:

x^7 - 7*x^5 - 2*x^4 + 12*x^3 + 6*x^2 - 4*x - 2

F@R@o:

x^7 - 7*x^5 - 2*x^4 + 13*x^3 + 6*x^2 - 5*x - 2

F@QGw:

x^7 - 7*x^5 - 2*x^4 + 11*x^3 + 2*x^2 - 4*x

FG_qw:

x^7 - 8*x^5 - 2*x^4 + 13*x^3 + 2*x^2 - 5*x

FGEJg:

x^7 - 8*x^5 - 2*x^4 + 13*x^3 + 6*x^2 - 4*x - 2

FG_Zg:

x^7 - 8*x^5 - 4*x^4 + 15*x^3 + 10*x^2 - 6*x - 4

F`Q@w:

x^7 - 8*x^5 - 2*x^4 + 16*x^3 + 4*x^2 - 7*x

comment: It has the same characteristic polynomial as F?L^?.

FA_hw:

x^7 - 8*x^5 - 4*x^4 + 12*x^3 + 6*x^2 - 4*x - 2

F@QHw:

x^7 - 8*x^5 - 4*x^4 + 14*x^3 + 8*x^2 - 5*x - 2

F`?^W:

x^7 - 9*x^5 - 4*x^4 + 16*x^3 + 8*x^2 - 6*x - 2

FCHJw:

x^7 - 9*x^5 - 6*x^4 + 13*x^3 + 8*x^2 - 4*x - 2

comment: It has the same characteristic polynomial as FAIXw.

FGEJw:

x^7 - 9*x^5 - 6*x^4 + 15*x^3 + 12*x^2 - 5*x - 4

F_Cnw:

x^7 - 10*x^5 - 8*x^4 + 16*x^3 + 14*x^2 - 5*x - 4

FGC\W:

x^7 - 8*x^5 - 4*x^4 + 12*x^3 + 8*x^2 - 3*x - 2

FGC^G:

x^7 - 8*x^5 - 4*x^4 + 15*x^3 + 14*x^2 - 2

FGC^W:

x^7 - 9*x^5 - 6*x^4 + 15*x^3 + 16*x^2 + x - 2

FGC\w:

x^7 - 9*x^5 - 8*x^4 + 10*x^3 + 12*x^2 - 2

FGC^w:

x^7 - 10*x^5 - 10*x^4 + 13*x^3 + 20*x^2 + 4*x - 2

comment: It has the same characteristic polynomial as FOxw`.

FK?}O:

x^7 - 8*x^5 + 17*x^3 - 4*x^2 - 10*x + 4

FAMRW:

x^7 - 9*x^5 - 2*x^4 + 13*x^3 + 2*x^2 - 4*x

F@QZo:

x^7 - 9*x^5 - 4*x^4 + 17*x^3 + 8*x^2 - 9*x - 4

F_W\g:

x^7 - 9*x^5 - 2*x^4 + 18*x^3 - 9*x + 2

FA_xw:

x^7 - 9*x^5 - 6*x^4 + 11*x^3 + 8*x^2 - 3*x - 2

FAIXw:

x^7 - 9*x^5 - 6*x^4 + 13*x^3 + 8*x^2 - 4*x - 2

comment: It has the same characteristic polynomial as FCHJw.

FCHiw:

x^7 - 9*x^5 - 6*x^4 + 14*x^3 + 10*x^2 - 4*x - 2

FG_yw:

x^7 - 9*x^5 - 4*x^4 + 14*x^3 + 2*x^2 - 4*x

FGC}W:

x^7 - 9*x^5 - 4*x^4 + 14*x^3 + 6*x^2 - 5*x - 2

FK?}W:

x^7 - 9*x^5 - 2*x^4 + 15*x^3 - 7*x + 2

FA_~o:

x^7 - 10*x^5 - 4*x^4 + 17*x^3 + 4*x^2 - 8*x

comment: It has the same characteristic polynomial as F?vw`.

F@`Zw:

x^7 - 10*x^5 - 8*x^4 + 13*x^3 + 10*x^2 - 3*x - 2

F@QZw:

x^7 - 10*x^5 - 8*x^4 + 15*x^3 + 12*x^2 - 6*x - 4

F_Dlw:

x^7 - 10*x^5 - 6*x^4 + 16*x^3 + 6*x^2 - 6*x

F@Q^w:

x^7 - 11*x^5 - 10*x^4 + 15*x^3 + 12*x^2 - 5*x - 2

F@LSW:

x^7 - 8*x^5 - 2*x^4 + 13*x^3 + 4*x^2 - 5*x - 2

F@Maw:

x^7 - 9*x^5 - 4*x^4 + 12*x^3 + 6*x^2 - 4*x - 2

FAStW:

x^7 - 9*x^5 - 4*x^4 + 17*x^3 + 10*x^2 - 4*x - 2

FGD\o:

x^7 - 9*x^5 - 4*x^4 + 17*x^3 + 6*x^2 - 9*x - 2

F@Lew:

x^7 - 10*x^5 - 6*x^4 + 16*x^3 + 10*x^2 - 5*x - 2

F@_zw:

x^7 - 10*x^5 - 10*x^4 + 10*x^3 + 12*x^2 - x - 2

FAG}w:

x^7 - 10*x^5 - 8*x^4 + 15*x^3 + 14*x^2 - x - 2

FGC}w:

x^7 - 10*x^5 - 8*x^4 + 13*x^3 + 10*x^2 - 4*x - 2

F@O~w:

x^7 - 11*x^5 - 12*x^4 + 12*x^3 + 16*x^2 - 2

comment: It has the same characteristic polynomial as FCLjw.

F`?}O:

x^7 - 8*x^5 - 4*x^4 + 17*x^3 + 16*x^2 - 2*x - 4

FODZo:

x^7 - 9*x^5 - 4*x^4 + 13*x^3 + 6*x^2 - 3*x

F_K^G:

x^7 - 9*x^5 - 4*x^4 + 18*x^3 + 14*x^2 - 2*x - 2

FGEZo:

x^7 - 9*x^5 - 6*x^4 + 17*x^3 + 18*x^2 - x - 4

FGEXw:

x^7 - 9*x^5 - 8*x^4 + 11*x^3 + 12*x^2 - x - 2

FGDkw:

x^7 - 9*x^5 - 6*x^4 + 16*x^3 + 16*x^2 - 2

F`?}W:

x^7 - 9*x^5 - 6*x^4 + 19*x^3 + 20*x^2 - 3*x - 6

F`C^W:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 16*x^2 - 2

FODZw:

x^7 - 10*x^5 - 10*x^4 + 11*x^3 + 14*x^2 - 2

comment: It has the same characteristic polynomial as FAK|W.

F_C~W:

x^7 - 10*x^5 - 8*x^4 + 18*x^3 + 20*x^2 - x - 4

FGEZw:

x^7 - 10*x^5 - 10*x^4 + 15*x^3 + 22*x^2 + 2*x - 4

F_C~w:

x^7 - 11*x^5 - 12*x^4 + 15*x^3 + 24*x^2 + 3*x - 4

F@`zo:

x^7 - 10*x^5 - 4*x^4 + 11*x^3 + 4*x^2 - 2*x

F@Q}o:

x^7 - 10*x^5 - 4*x^4 + 18*x^3 + 8*x^2 - 4*x

F@P|o:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 6*x - 4

F_D|o:

x^7 - 10*x^5 - 4*x^4 + 18*x^3 + 2*x^2 - 9*x + 2

F@`~o:

x^7 - 11*x^5 - 6*x^4 + 16*x^3 + 8*x^2 - 4*x

F@`zw:

x^7 - 11*x^5 - 12*x^4 + 9*x^3 + 14*x^2 + x - 2

F@Q}w:

x^7 - 11*x^5 - 10*x^4 + 16*x^3 + 16*x^2 - x - 2

F@P|w:

x^7 - 11*x^5 - 12*x^4 + 13*x^3 + 18*x^2 - x - 4

F_D|w:

x^7 - 11*x^5 - 10*x^4 + 14*x^3 + 10*x^2 - 4*x

comment: It has the same characteristic polynomial as F@Tlw.

F@`~w:

x^7 - 12*x^5 - 14*x^4 + 12*x^3 + 18*x^2 + x - 2

comment: It has the same characteristic polynomial as FA]rw.

F@P~o:

x^7 - 11*x^5 - 8*x^4 + 15*x^3 + 12*x^2 - 5*x - 4

F@P~w:

x^7 - 12*x^5 - 16*x^4 + 9*x^3 + 20*x^2 + 2*x - 4

F@R~o:

x^7 - 12*x^5 - 8*x^4 + 13*x^3 + 8*x^2 - 2*x

F@R~w:

x^7 - 13*x^5 - 18*x^4 + 7*x^3 + 20*x^2 + 5*x - 2

FHQSO:

x^7 - 7*x^5 + 14*x^3 - 7*x - 2

comment: This is the cycle $C_7$.

FGSkg:

x^7 - 8*x^5 + 12*x^3 - 3*x

FCXPW:

x^7 - 8*x^5 - 2*x^4 + 14*x^3 + 4*x^2 - 5*x

Fk?gw:

x^7 - 8*x^5 - 2*x^4 + 17*x^3 + 6*x^2 - 10*x - 4

FK_qW:

x^7 - 8*x^5 + 15*x^3 - 2*x^2 - 5*x

FGC{o:

x^7 - 8*x^5 - 4*x^4 + 13*x^3 + 8*x^2 - 4*x - 2

FICkW:

x^7 - 8*x^5 - 2*x^4 + 16*x^3 + 2*x^2 - 9*x + 2

FKHGw:

x^7 - 8*x^5 - 2*x^4 + 14*x^3 + 2*x^2 - 4*x

F?L\_:

x^7 - 8*x^5 - 2*x^4 + 13*x^3 + 2*x^2 - 3*x

FGK]G:

x^7 - 8*x^5 - 2*x^4 + 16*x^3 + 4*x^2 - 8*x - 2

F_StW:

x^7 - 9*x^5 - 2*x^4 + 16*x^3 + 4*x^2 - 6*x - 2

FGUPw:

x^7 - 9*x^5 - 4*x^4 + 15*x^3 + 6*x^2 - 5*x

FOLQw:

x^7 - 9*x^5 - 6*x^4 + 15*x^3 + 12*x^2 - 3*x - 2

FoCiw:

x^7 - 9*x^5 - 4*x^4 + 18*x^3 + 8*x^2 - 8*x - 2

comment: It has the same characteristic polynomial as F@LuO.

FKG]W:

x^7 - 9*x^5 - 2*x^4 + 16*x^3 - 3*x

FAN@w:

x^7 - 9*x^5 - 4*x^4 + 15*x^3 + 8*x^2 - 4*x - 2

FAYPw:

x^7 - 9*x^5 - 4*x^4 + 17*x^3 + 6*x^2 - 8*x

comment: It has the same characteristic polynomial as Fo?yw.

F_YPw:

x^7 - 9*x^5 - 4*x^4 + 20*x^3 + 10*x^2 - 13*x - 6

F@YPw:

x^7 - 9*x^5 - 6*x^4 + 14*x^3 + 10*x^2 - 3*x - 2

FaG\w:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 10*x^2 - 4*x - 2

FB_mw:

x^7 - 10*x^5 - 6*x^4 + 19*x^3 + 12*x^2 - 9*x - 4

F@YRw:

x^7 - 10*x^5 - 8*x^4 + 16*x^3 + 14*x^2 - 4*x - 2

F@YVw:

x^7 - 11*x^5 - 10*x^4 + 18*x^3 + 18*x^2 - 5*x - 4

FGLSW:

x^7 - 8*x^5 + 14*x^3 - 4*x^2 - 5*x + 2

F@Tcw:

x^7 - 9*x^5 - 2*x^4 + 15*x^3 - 2*x^2 - 6*x + 2

FGLSw:

x^7 - 9*x^5 - 4*x^4 + 17*x^3 + 4*x^2 - 10*x + 2

F@Tdw:

x^7 - 10*x^5 - 6*x^4 + 16*x^3 + 4*x^2 - 9*x + 2

F@Tfw:

x^7 - 11*x^5 - 10*x^4 + 15*x^3 + 8*x^2 - 10*x + 2

F@Umg:

x^7 - 10*x^5 - 2*x^4 + 14*x^3 - 4*x

F@Xsw:

x^7 - 10*x^5 - 4*x^4 + 13*x^3 + 2*x^2 - 4*x

F@hqw:

x^7 - 10*x^5 - 6*x^4 + 15*x^3 + 8*x^2 - 4*x - 2

FBJKw:

x^7 - 10*x^5 - 4*x^4 + 18*x^3 + 2*x^2 - 6*x

F@Y^_:

x^7 - 10*x^5 - 2*x^4 + 19*x^3 - 6*x^2 - 5*x + 2

F@Lkw:

x^7 - 10*x^5 - 8*x^4 + 11*x^3 + 8*x^2 - 3*x - 2

F@h^g:

x^7 - 11*x^5 - 6*x^4 + 16*x^3 + 2*x^2 - 4*x

F@Y]w:

x^7 - 11*x^5 - 8*x^4 + 15*x^3 + 8*x^2 - 5*x - 2

F@Ujw:

x^7 - 11*x^5 - 10*x^4 + 12*x^3 + 10*x^2 - 3*x - 2

F@Y^w:

x^7 - 12*x^5 - 12*x^4 + 13*x^3 + 10*x^2 - 3*x - 2

FHTcw:

x^7 - 10*x^5 - 4*x^4 + 18*x^3 + 2*x^2 - 4*x

F@Tkw:

x^7 - 10*x^5 - 6*x^4 + 14*x^3 + 4*x^2 - 5*x

FHO}w:

x^7 - 11*x^5 - 8*x^4 + 15*x^3 + 6*x^2 - 5*x

FALlw:

x^7 - 11*x^5 - 10*x^4 + 12*x^3 + 8*x^2 - 5*x

F@Tlw:

x^7 - 11*x^5 - 10*x^4 + 14*x^3 + 10*x^2 - 4*x

comment: It has the same characteristic polynomial as F_D|w.

FGL^w:

x^7 - 12*x^5 - 14*x^4 + 10*x^3 + 10*x^2 - 4*x

FAdl_:

x^7 - 9*x^5 + 17*x^3 - 6*x^2 - 5*x + 2

F@U^?:

x^7 - 9*x^5 - 2*x^4 + 21*x^3 - 16*x + 6

FBebW:

x^7 - 10*x^5 - 2*x^4 + 17*x^3 - 2*x^2 - 4*x

F@fbo:

x^7 - 10*x^5 - 4*x^4 + 21*x^3 + 4*x^2 - 13*x + 2

FHQZo:

x^7 - 10*x^5 - 6*x^4 + 18*x^3 + 10*x^2 - 7*x - 2

comment: It has the same characteristic polynomial as FHQ[w.

FBO|W:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 6*x^2 - 8*x

FHQ[w:

x^7 - 10*x^5 - 6*x^4 + 18*x^3 + 10*x^2 - 7*x - 2

comment: It has the same characteristic polynomial as FHQZo.

FHQ^o:

x^7 - 11*x^5 - 6*x^4 + 19*x^3 + 6*x^2 - 8*x

comment: It has the same characteristic polynomial as F@N^O.

FD`jw:

x^7 - 11*x^5 - 8*x^4 + 18*x^3 + 10*x^2 - 7*x - 2

F@jRw:

x^7 - 11*x^5 - 8*x^4 + 20*x^3 + 10*x^2 - 12*x

FHQZw:

x^7 - 11*x^5 - 10*x^4 + 17*x^3 + 14*x^2 - 8*x - 2

FHQ^w:

x^7 - 12*x^5 - 12*x^4 + 18*x^3 + 16*x^2 - 9*x - 2

F@W}g:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 8*x^2 - 7*x - 2

F@L[w:

x^7 - 10*x^5 - 10*x^4 + 10*x^3 + 10*x^2 - 3*x - 2

F@T\W:

x^7 - 10*x^5 - 6*x^4 + 12*x^3 + 8*x^2 - 3*x - 2

F@Lmw:

x^7 - 11*x^5 - 10*x^4 + 14*x^3 + 12*x^2 - 3*x - 2

F@MZw:

x^7 - 11*x^5 - 14*x^4 + 6*x^3 + 12*x^2 - 2

FAS|w:

x^7 - 11*x^5 - 12*x^4 + 11*x^3 + 16*x^2 + x - 2

FAK~W:

x^7 - 11*x^5 - 10*x^4 + 12*x^3 + 10*x^2 - 4*x - 2

F@L^w:

x^7 - 12*x^5 - 16*x^4 + 7*x^3 + 14*x^2 - 2

F@Vcw:

x^7 - 10*x^5 - 4*x^4 + 20*x^3 + 2*x^2 - 13*x + 4

F@U^W:

x^7 - 11*x^5 - 8*x^4 + 17*x^3 + 6*x^2 - 10*x + 2

F@UZw:

x^7 - 11*x^5 - 12*x^4 + 11*x^3 + 12*x^2 - 4*x - 2

F@U^w:

x^7 - 12*x^5 - 14*x^4 + 12*x^3 + 12*x^2 - 7*x

comment: It has the same characteristic polynomial as F?]}w.

FHQ}o:

x^7 - 11*x^5 - 4*x^4 + 20*x^3 - 2*x^2 - 4*x

FGN^o:

x^7 - 12*x^5 - 8*x^4 + 16*x^3 + 4*x^2 - 4*x

FGU|w:

x^7 - 12*x^5 - 12*x^4 + 12*x^3 + 12*x^2 - 3*x - 2

FGL}w:

x^7 - 12*x^5 - 14*x^4 + 11*x^3 + 14*x^2 - 3*x - 2

FHQ}w:

x^7 - 12*x^5 - 10*x^4 + 17*x^3 + 8*x^2 - 5*x - 2

FGN^w:

x^7 - 13*x^5 - 16*x^4 + 11*x^3 + 14*x^2 - 3*x - 2

F@d~o:

x^7 - 12*x^5 - 10*x^4 + 15*x^3 + 8*x^2 - 4*x

F@Vlw:

x^7 - 12*x^5 - 12*x^4 + 16*x^3 + 14*x^2 - 7*x - 2

F@dzw:

x^7 - 12*x^5 - 16*x^4 + 6*x^3 + 14*x^2 + x - 2

F@T|w:

x^7 - 12*x^5 - 16*x^4 + 8*x^3 + 16*x^2 - 2

F@U}w:

x^7 - 12*x^5 - 14*x^4 + 13*x^3 + 18*x^2 - 2*x - 4

FGN\w:

x^7 - 12*x^5 - 12*x^4 + 14*x^3 + 10*x^2 - 6*x

FAM~w:

x^7 - 13*x^5 - 18*x^4 + 8*x^3 + 16*x^2 - x - 2

F@T~o:

x^7 - 12*x^5 - 12*x^4 + 12*x^3 + 10*x^2 - 3*x - 2

F@T~w:

x^7 - 13*x^5 - 20*x^4 + 3*x^3 + 14*x^2 - 2

F@V~o:

x^7 - 13*x^5 - 12*x^4 + 11*x^3 + 4*x^2 - 2*x

F@V~w:

x^7 - 14*x^5 - 22*x^4 + 2*x^3 + 14*x^2 + x - 2

FCX_w:

x^7 - 8*x^5 + 10*x^3

FK`_w:

x^7 - 8*x^5 - 2*x^4 + 15*x^3 + 8*x^2 - 2*x

F_KuW:

x^7 - 9*x^5 - 2*x^4 + 14*x^3 + 8*x^2

FOTPw:

x^7 - 9*x^5 - 4*x^4 + 13*x^3 + 4*x^2 - 2*x

F`CmW:

x^7 - 9*x^5 - 4*x^4 + 18*x^3 + 10*x^2 - 4*x

comment: It has the same characteristic polynomial as F@Tl_.

F`G]w:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 2*x

F_Krw:

x^7 - 10*x^5 - 8*x^4 + 12*x^3 + 8*x^2

F_Kvw:

x^7 - 11*x^5 - 10*x^4 + 16*x^3 + 16*x^2

comment: It has the same characteristic polynomial as FKWyw and FKcyw.

F?\t_:

x^7 - 9*x^5 + 10*x^3

FK_yo:

x^7 - 9*x^5 + 15*x^3 - 4*x^2 - 2*x

F@\cg:

x^7 - 9*x^5 - 2*x^4 + 16*x^3 - 5*x

F`KqW:

x^7 - 9*x^5 - 4*x^4 + 14*x^3 + 8*x^2 - 2*x

FCdj_:

x^7 - 9*x^5 - 2*x^4 + 19*x^3 + 4*x^2 - 8*x

FDhaw:

x^7 - 10*x^5 - 2*x^4 + 15*x^3 + 4*x^2 - 2*x

FBZ@w:

x^7 - 10*x^5 - 4*x^4 + 14*x^3 + 4*x^2 - 2*x

FDUbW:

x^7 - 10*x^5 - 4*x^4 + 21*x^3 + 6*x^2 - 11*x

F`IZo:

x^7 - 10*x^5 - 4*x^4 + 19*x^3 + 4*x^2 - 8*x

FI_xw:

x^7 - 10*x^5 - 6*x^4 + 13*x^3 + 8*x^2 - 2*x

FaG{w:

x^7 - 10*x^5 - 6*x^4 + 18*x^3 + 12*x^2 - 3*x

comment: It has the same characteristic polynomial as FJQHw.

F`H[w:

x^7 - 10*x^5 - 4*x^4 + 16*x^3

FBZDw:

x^7 - 11*x^5 - 6*x^4 + 19*x^3 + 8*x^2 - 8*x

comment: It has the same characteristic polynomial as F@h}o.

FSOzw:

x^7 - 11*x^5 - 8*x^4 + 16*x^3 + 12*x^2

FI_zw:

x^7 - 11*x^5 - 10*x^4 + 13*x^3 + 12*x^2

FB`lw:

x^7 - 11*x^5 - 8*x^4 + 18*x^3 + 12*x^2 - 5*x

F`H\w:

x^7 - 11*x^5 - 8*x^4 + 16*x^3 + 8*x^2 - 2*x

FI_~w:

x^7 - 12*x^5 - 12*x^4 + 16*x^3 + 16*x^2 - 2*x

FKcqW:

x^7 - 9*x^5 - 2*x^4 + 17*x^3 + 6*x^2 - 5*x

F@Tl_:

x^7 - 9*x^5 - 4*x^4 + 18*x^3 + 10*x^2 - 4*x

comment: It has the same characteristic polynomial as FCmW`.

FAdtO:

x^7 - 9*x^5 - 4*x^4 + 21*x^3 + 14*x^2 - 9*x - 6

F@LuO:

x^7 - 9*x^5 - 4*x^4 + 18*x^3 + 8*x^2 - 8*x - 2

comment: It has the same characteristic polynomial as FoCiw.

F`Maw:

x^7 - 10*x^5 - 4*x^4 + 17*x^3 + 10*x^2 - 4*x - 2

FDdbW:

x^7 - 10*x^5 - 6*x^4 + 21*x^3 + 20*x^2 - 2

FJQHw:

x^7 - 10*x^5 - 6*x^4 + 18*x^3 + 12*x^2 - 3*x

comment: It has the same characteristic polynomial as FaG{w.

F@nBg:

x^7 - 10*x^5 - 6*x^4 + 23*x^3 + 18*x^2 - 12*x - 10

F`Oxw:

x^7 - 10*x^5 - 10*x^4 + 13*x^3 + 20*x^2 + 4*x - 2

comment: It has the same characteristic polynomial as FGC^w.

FoCyw:

x^7 - 10*x^5 - 8*x^4 + 18*x^3 + 18*x^2 - 5*x - 6

FJQLw:

x^7 - 11*x^5 - 8*x^4 + 21*x^3 + 22*x^2 - x - 4

F`_zw:

x^7 - 11*x^5 - 10*x^4 + 16*x^3 + 20*x^2 + 2*x - 2

FDPlw:

x^7 - 11*x^5 - 10*x^4 + 20*x^3 + 26*x^2 + 4*x - 2

FGdrw:

x^7 - 11*x^5 - 12*x^4 + 15*x^3 + 24*x^2 + 5*x - 2

F@ptw:

x^7 - 11*x^5 - 10*x^4 + 20*x^3 + 24*x^2 - 4*x - 8

FGdvw:

x^7 - 12*x^5 - 14*x^4 + 18*x^3 + 32*x^2 + 7*x - 4

F@]eg:

x^7 - 10*x^5 - 4*x^4 + 21*x^3 + 8*x^2 - 8*x - 2

F@X\g:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 10*x^2 - 5*x

F@UuW:

x^7 - 10*x^5 - 6*x^4 + 22*x^3 + 16*x^2 - 12*x - 8

FHFKw:

x^7 - 10*x^5 - 6*x^4 + 20*x^3 + 10*x^2 - 12*x - 2

FB_zW:

x^7 - 10*x^5 - 6*x^4 + 15*x^3 + 6*x^2 - 3*x

FAgzg:

x^7 - 10*x^5 - 8*x^4 + 17*x^3 + 18*x^2 - 2

FEHkw:

x^7 - 10*x^5 - 6*x^4 + 20*x^3 + 16*x^2 - 5*x - 4

F`Dkw:

x^7 - 10*x^5 - 4*x^4 + 16*x^3 + 4*x^2 - 5*x

FAK|W:

x^7 - 10*x^5 - 10*x^4 + 11*x^3 + 14*x^2 - 2

comment: It has the same characteristic polynomial as FODZw.

FCLZW:

x^7 - 10*x^5 - 8*x^4 + 16*x^3 + 12*x^2 - 7*x - 2

F@S}W:

x^7 - 10*x^5 - 8*x^4 + 16*x^3 + 16*x^2 - 2

FGL[w:

x^7 - 10*x^5 - 8*x^4 + 14*x^3 + 10*x^2 - 4*x

F_YXw:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 10*x^2 - 7*x - 4

F@huw:

x^7 - 11*x^5 - 8*x^4 + 20*x^3 + 14*x^2 - 9*x - 4

FDO~W:

x^7 - 11*x^5 - 8*x^4 + 18*x^3 + 14*x^2 - 2*x - 2

FCLjw:

x^7 - 11*x^5 - 12*x^4 + 12*x^3 + 16*x^2 - 2

comment: It has the same characteristic polynomial as F@O~w.

FAMjw:

x^7 - 11*x^5 - 12*x^4 + 14*x^3 + 20*x^2 + x - 2

F@qZw:

x^7 - 11*x^5 - 10*x^4 + 19*x^3 + 20*x^2 - 6*x - 6

F_S|w:

x^7 - 11*x^5 - 10*x^4 + 15*x^3 + 14*x^2 - 4*x - 2

FGc~w:

x^7 - 12*x^5 - 14*x^4 + 15*x^3 + 22*x^2 - x - 4

F`KuW:

x^7 - 10*x^5 - 6*x^4 + 19*x^3 + 22*x^2 + 6*x

F`Gyw:

x^7 - 10*x^5 - 8*x^4 + 13*x^3 + 12*x^2

comment: It has the same characteristic polynomial as F_?~w.

F`FHw:

x^7 - 10*x^5 - 8*x^4 + 20*x^3 + 26*x^2 + 5*x - 2

FOLYw:

x^7 - 10*x^5 - 10*x^4 + 12*x^3 + 16*x^2 + x - 2

F_oxw:

x^7 - 10*x^5 - 8*x^4 + 17*x^3 + 24*x^2 + 8*x

F`G}w:

x^7 - 11*x^5 - 10*x^4 + 18*x^3 + 26*x^2 + 8*x

F_Kzw:

x^7 - 11*x^5 - 14*x^4 + 8*x^3 + 18*x^2 + 6*x

F_K}w:

x^7 - 11*x^5 - 12*x^4 + 17*x^3 + 30*x^2 + 9*x - 2

F_K~w:

x^7 - 12*x^5 - 16*x^4 + 13*x^3 + 32*x^2 + 14*x

F@Neo:

x^7 - 10*x^5 - 4*x^4 + 21*x^3 + 6*x^2 - 10*x

F@NMg:

x^7 - 10*x^5 - 6*x^4 + 20*x^3 + 16*x^2

F@L^G:

x^7 - 10*x^5 - 6*x^4 + 17*x^3 + 12*x^2 - 4*x - 2

FB`kw:

x^7 - 10*x^5 - 4*x^4 + 16*x^3 + 8*x^2 - 2*x

F@ozg:

x^7 - 10*x^5 - 8*x^4 + 15*x^3 + 16*x^2 - 2

F@K}W:

x^7 - 10*x^5 - 10*x^4 + 11*x^3 + 18*x^2 + 6*x

F@NNg:

x^7 - 11*x^5 - 8*x^4 + 20*x^3 + 16*x^2 - 2*x

F@o~g:

x^7 - 11*x^5 - 8*x^4 + 16*x^3 + 14*x^2

F@o}w:

x^7 - 11*x^5 - 10*x^4 + 17*x^3 + 22*x^2 + 6*x

F@NJw:

x^7 - 11*x^5 - 12*x^4 + 14*x^3 + 22*x^2 + 4*x - 2

F@o~w:

x^7 - 12*x^5 - 14*x^4 + 15*x^3 + 26*x^2 + 8*x

FK`zo:

x^7 - 11*x^5 - 4*x^4 + 14*x^3 + 8*x^2

FK`~o:

x^7 - 12*x^5 - 8*x^4 + 19*x^3 + 14*x^2 - 2*x

FK`zw:

x^7 - 12*x^5 - 12*x^4 + 13*x^3 + 20*x^2 + 6*x

FK`~w:

x^7 - 13*x^5 - 16*x^4 + 14*x^3 + 26*x^2 + 8*x

FI`|o:

x^7 - 11*x^5 - 6*x^4 + 20*x^3 + 14*x^2

FC\ng:

x^7 - 12*x^5 - 10*x^4 + 18*x^3 + 16*x^2 - 2*x

FI`|w:

x^7 - 12*x^5 - 12*x^4 + 17*x^3 + 22*x^2 + 6*x

FCXzw:

x^7 - 12*x^5 - 16*x^4 + 7*x^3 + 18*x^2 + 6*x

FGezw:

x^7 - 12*x^5 - 14*x^4 + 16*x^3 + 26*x^2 + 4*x - 2

F_L|w:

x^7 - 12*x^5 - 14*x^4 + 12*x^3 + 16*x^2

comment: It has the same characteristic polynomial as FHUZw.

FCX~w:

x^7 - 13*x^5 - 18*x^4 + 11*x^3 + 26*x^2 + 8*x

FGd~_:

x^7 - 11*x^5 - 6*x^4 + 22*x^3 + 10*x^2 - 10*x - 2

FG]^g:

x^7 - 12*x^5 - 10*x^4 + 20*x^3 + 18*x^2 - 5*x - 4

FGd~g:

x^7 - 12*x^5 - 12*x^4 + 17*x^3 + 20*x^2 - 2

FGdzw:

x^7 - 12*x^5 - 16*x^4 + 11*x^3 + 26*x^2 + 8*x - 2

F@p|w:

x^7 - 12*x^5 - 14*x^4 + 18*x^3 + 28*x^2 - 3*x - 10

FGd~w:

x^7 - 13*x^5 - 18*x^4 + 13*x^3 + 30*x^2 + 7*x - 4

F_N~o:

x^7 - 13*x^5 - 12*x^4 + 16*x^3 + 16*x^2

F_N~w:

x^7 - 14*x^5 - 22*x^4 + 7*x^3 + 30*x^2 + 14*x

FEOhW:

x^7 - 8*x^5 - 4*x^4 + 14*x^3 + 10*x^2 - 3*x - 2

FGW[g:

x^7 - 8*x^5 - 4*x^4 + 16*x^3 + 14*x^2 - x - 2

F?K}_:

x^7 - 8*x^5 - 4*x^4 + 13*x^3 + 10*x^2

FoCZW:

x^7 - 9*x^5 - 4*x^4 + 16*x^3 + 12*x^2

FWCYw:

x^7 - 9*x^5 - 8*x^4 + 13*x^3 + 18*x^2 + 3*x - 2

F_opw:

x^7 - 9*x^5 - 6*x^4 + 18*x^3 + 22*x^2 + 6*x

FAU`w:

x^7 - 9*x^5 - 6*x^4 + 17*x^3 + 18*x^2 + x - 2

F@N@w:

x^7 - 9*x^5 - 8*x^4 + 12*x^3 + 18*x^2 + 6*x

FoCZw:

x^7 - 10*x^5 - 8*x^4 + 15*x^3 + 20*x^2 + 6*x

FEGmw:

x^7 - 10*x^5 - 8*x^4 + 19*x^3 + 26*x^2 + 8*x

F@NBw:

x^7 - 10*x^5 - 10*x^4 + 16*x^3 + 26*x^2 + 7*x - 2

F@NFw:

x^7 - 11*x^5 - 12*x^4 + 18*x^3 + 34*x^2 + 14*x

F@K}w:

x^7 - 11*x^5 - 14*x^4 + 6*x^3 + 16*x^2 + 6*x

F@K~w:

x^7 - 12*x^5 - 20*x^4 - 3*x^3 + 12*x^2 + 6*x

F@N^o:

x^7 - 12*x^5 - 10*x^4 + 13*x^3 + 10*x^2 - 2*x

F@N]w:

x^7 - 12*x^5 - 14*x^4 + 11*x^3 + 22*x^2 + 8*x

F@N^W:

x^7 - 12*x^5 - 12*x^4 + 16*x^3 + 16*x^2

F@L}w:

x^7 - 12*x^5 - 16*x^4 + 8*x^3 + 18*x^2 + 3*x - 2

F@N^w:

x^7 - 13*x^5 - 18*x^4 + 8*x^3 + 20*x^2 + 6*x

F@L~o:

x^7 - 12*x^5 - 14*x^4 + 7*x^3 + 12*x^2 - 2

F@L|w:

x^7 - 12*x^5 - 20*x^4 - 2*x^3 + 12*x^2 + 3*x - 2

F@L~w:

x^7 - 13*x^5 - 22*x^4 - 2*x^3 + 14*x^2 + 4*x - 2

F@N~o:

x^7 - 13*x^5 - 14*x^4 + 6*x^3 + 8*x^2

F@N~w:

x^7 - 14*x^5 - 24*x^4 - 3*x^3 + 16*x^2 + 8*x

FBY^G:

x^7 - 11*x^5 - 2*x^4 + 12*x^3

FIK}W:

x^7 - 11*x^5 - 6*x^4 + 10*x^3 + 4*x^2 - 2*x

FIo|g:

x^7 - 11*x^5 - 4*x^4 + 18*x^3 - 4*x^2 - 2*x

F@\sw:

x^7 - 11*x^5 - 8*x^4 + 11*x^3 + 4*x^2 - 2*x

FC\rW:

x^7 - 11*x^5 - 8*x^4 + 12*x^3 + 8*x^2

FCdzo:

x^7 - 11*x^5 - 6*x^4 + 12*x^3 + 8*x^2

FAY|o:

x^7 - 11*x^5 - 4*x^4 + 13*x^3 - 2*x

FINLw:

x^7 - 12*x^5 - 8*x^4 + 14*x^3 + 4*x^2 - 2*x

FBYZw:

x^7 - 12*x^5 - 12*x^4 + 8*x^3 + 8*x^2

FAmrw:

x^7 - 12*x^5 - 10*x^4 + 13*x^3 + 8*x^2 - 2*x

FC\vW:

x^7 - 12*x^5 - 8*x^4 + 14*x^3

FBY^w:

x^7 - 13*x^5 - 14*x^4 + 10*x^3 + 8*x^2

FBY^?:

x^7 - 10*x^5 + 16*x^3 - 8*x^2

FLr@w:

x^7 - 11*x^5 - 2*x^4 + 17*x^3 - 4*x^2 - 2*x

FF`jW:

x^7 - 11*x^5 - 6*x^4 + 20*x^3 + 6*x^2 - 10*x

FAM~O:

x^7 - 11*x^5 - 6*x^4 + 19*x^3 + 2*x^2 - 9*x + 2

F_L|o:

x^7 - 11*x^5 - 8*x^4 + 19*x^3 + 10*x^2 - 10*x

F@N^O:

x^7 - 11*x^5 - 6*x^4 + 19*x^3 + 6*x^2 - 8*x

comment: It has the same characteristic polynomial as FHQ^o.

Fk_zw:

x^7 - 12*x^5 - 8*x^4 + 19*x^3 + 6*x^2 - 8*x

comment: It has the same characteristic polynomial as FA]~_.

FC^bw:

x^7 - 12*x^5 - 10*x^4 + 18*x^3 + 8*x^2 - 8*x

FGnRw:

x^7 - 12*x^5 - 10*x^4 + 20*x^3 + 10*x^2 - 13*x + 2

F_]vw:

x^7 - 13*x^5 - 14*x^4 + 17*x^3 + 14*x^2 - 10*x

F_|tg:

x^7 - 12*x^5 - 6*x^4 + 20*x^3

FFo~W:

x^7 - 13*x^5 - 10*x^4 + 15*x^3 + 6*x^2 - 2*x

FWN]w:

x^7 - 13*x^5 - 12*x^4 + 12*x^3 + 10*x^2 - 2*x

FC^vW:

x^7 - 13*x^5 - 12*x^4 + 16*x^3 + 8*x^2 - 2*x

FENnw:

x^7 - 14*x^5 - 18*x^4 + 9*x^3 + 14*x^2

FBd~W:

x^7 - 13*x^5 - 14*x^4 + 13*x^3 + 14*x^2

FC\zw:

x^7 - 13*x^5 - 20*x^4 + 14*x^2 + 6*x

FAmzw:

x^7 - 13*x^5 - 18*x^4 + 9*x^3 + 22*x^2 + 5*x - 2

FC\~W:

x^7 - 13*x^5 - 16*x^4 + 10*x^3 + 12*x^2 - 2*x

FC\~w:

x^7 - 14*x^5 - 22*x^4 + 3*x^3 + 18*x^2 + 6*x

FBNmw:

x^7 - 13*x^5 - 14*x^4 + 15*x^3 + 14*x^2 - 3*x - 2

F@t~g:

x^7 - 13*x^5 - 14*x^4 + 13*x^3 + 12*x^2 - 4*x

F@\}w:

x^7 - 13*x^5 - 20*x^4 + 4*x^3 + 18*x^2 + 4*x - 2

F@]}w:

x^7 - 13*x^5 - 18*x^4 + 11*x^3 + 22*x^2 - 2*x - 6

F@^^w:

x^7 - 14*x^5 - 22*x^4 + 5*x^3 + 20*x^2 + 3*x - 2

FG]}w:

x^7 - 13*x^5 - 16*x^4 + 14*x^3 + 18*x^2 - 4*x

comment: It has the same characteristic polynomial as FHU^w.

F_]~w:

x^7 - 14*x^5 - 20*x^4 + 8*x^3 + 16*x^2

F@v~w:

x^7 - 15*x^5 - 26*x^4 - 2*x^3 + 16*x^2 + 6*x

FBejW:

x^7 - 11*x^5 - 6*x^4 + 17*x^3 + 6*x^2 - 4*x

FEXhw:

x^7 - 11*x^5 - 10*x^4 + 14*x^3 + 16*x^2 - 2

FELlW:

x^7 - 11*x^5 - 8*x^4 + 19*x^3 + 12*x^2 - 8*x - 2

FGlug:

x^7 - 11*x^5 - 6*x^4 + 22*x^3 + 6*x^2 - 13*x + 2

FBUlW:

x^7 - 11*x^5 - 8*x^4 + 19*x^3 + 20*x^2 + x - 2

FIS|W:

x^7 - 11*x^5 - 8*x^4 + 16*x^3 + 8*x^2 - 3*x

FBMmW:

x^7 - 11*x^5 - 8*x^4 + 21*x^3 + 16*x^2 - 9*x - 6

FJQ\W:

x^7 - 11*x^5 - 6*x^4 + 22*x^3 + 10*x^2 - 4*x

FAd|o:

x^7 - 11*x^5 - 8*x^4 + 18*x^3 + 12*x^2 - 3*x - 2

FAizo:

x^7 - 11*x^5 - 8*x^4 + 21*x^3 + 18*x^2 - 4*x - 2

F@L}o:

x^7 - 11*x^5 - 10*x^4 + 13*x^3 + 14*x^2 - x - 2

FG[}g:

x^7 - 11*x^5 - 8*x^4 + 16*x^3 + 10*x^2 - 4*x - 2

F@h}o:

x^7 - 11*x^5 - 6*x^4 + 19*x^3 + 8*x^2 - 8*x

comment: It has the same characteristic polynomial as FBZDw.

FEW~W:

x^7 - 12*x^5 - 10*x^4 + 16*x^3 + 12*x^2 - 4*x

FHNMw:

x^7 - 12*x^5 - 10*x^4 + 18*x^3 + 16*x^2 - x - 2

FClrw:

x^7 - 12*x^5 - 12*x^4 + 17*x^3 + 20*x^2 + x - 2

FA]rw:

x^7 - 12*x^5 - 14*x^4 + 12*x^3 + 18*x^2 + x - 2

comment: It has the same characteristic polynomial as F@~w`.

F@nRw:

x^7 - 12*x^5 - 12*x^4 + 17*x^3 + 18*x^2 - 5*x - 4

FG^Tw:

x^7 - 12*x^5 - 10*x^4 + 20*x^3 + 14*x^2 - 6*x

FA]vw:

x^7 - 13*x^5 - 16*x^4 + 14*x^3 + 22*x^2 + x - 2

FG\sw:

x^7 - 11*x^5 - 8*x^4 + 16*x^3 + 12*x^2 - 2*x

FIS|w:

x^7 - 12*x^5 - 12*x^4 + 10*x^3 + 8*x^2 - 3*x

FA\tw:

x^7 - 12*x^5 - 12*x^4 + 12*x^3 + 8*x^2 - 2*x

F@\tw:

x^7 - 12*x^5 - 14*x^4 + 7*x^3 + 8*x^2 - 2*x

F@\vw:

x^7 - 13*x^5 - 18*x^4 + 4*x^3 + 8*x^2 - 2*x

FHL[w:

x^7 - 11*x^5 - 10*x^4 + 13*x^3 + 10*x^2 - 3*x

F@T|o:

x^7 - 11*x^5 - 10*x^4 + 15*x^3 + 14*x^2 - 3*x - 2

F@]uW:

x^7 - 11*x^5 - 8*x^4 + 23*x^3 + 20*x^2 - 13*x - 12

F@L|o:

x^7 - 11*x^5 - 14*x^4 + 7*x^3 + 16*x^2 + 3*x - 2

FHM]w:

x^7 - 12*x^5 - 12*x^4 + 15*x^3 + 18*x^2 - 2*x - 4

F@]uw:

x^7 - 12*x^5 - 12*x^4 + 19*x^3 + 20*x^2 - 8*x - 8

F@]rw:

x^7 - 12*x^5 - 16*x^4 + 9*x^3 + 20*x^2 + 4*x - 2

F@]vw:

x^7 - 13*x^5 - 18*x^4 + 11*x^3 + 24*x^2 + x - 6

F@^vo:

x^7 - 13*x^5 - 12*x^4 + 12*x^3 + 8*x^2 - 4*x

FHN]w:

x^7 - 13*x^5 - 14*x^4 + 11*x^3 + 16*x^2 + x - 2

F@l~g:

x^7 - 13*x^5 - 16*x^4 + 10*x^3 + 14*x^2 - 2*x - 2

F@^vw:

x^7 - 14*x^5 - 20*x^4 + 6*x^3 + 16*x^2 + x - 2

F@\~g:

x^7 - 13*x^5 - 18*x^4 + 5*x^3 + 14*x^2 + x - 2

F@\|w:

x^7 - 13*x^5 - 22*x^4 - x^3 + 16*x^2 + 5*x - 2

F@\~w:

x^7 - 14*x^5 - 26*x^4 - 7*x^3 + 12*x^2 + 4*x - 2

F@]~w:

x^7 - 14*x^5 - 24*x^4 + 18*x^2 + 3*x - 4

F@^~w:

x^7 - 15*x^5 - 28*x^4 - 7*x^3 + 14*x^2 + 5*x - 2

F@~vg:

x^7 - 14*x^5 - 14*x^4 + 7*x^3 + 6*x^2 - 2*x

F@~uw:

x^7 - 14*x^5 - 16*x^4 + 10*x^3 + 8*x^2

F@^~o:

x^7 - 14*x^5 - 18*x^4 + 5*x^3 + 8*x^2 - 2*x

F@~vw:

x^7 - 15*x^5 - 22*x^4 + 8*x^2

F@~~w:

x^7 - 16*x^5 - 32*x^4 - 15*x^3 + 8*x^2 + 6*x

comment: It has the same characteristic polynomial as FJ^~o.

FBY~o:

x^7 - 13*x^5 - 12*x^4 + 14*x^3 + 4*x^2 - 2*x

FDhzw:

x^7 - 13*x^5 - 16*x^4 + 8*x^3 + 12*x^2

FBY}w:

x^7 - 13*x^5 - 14*x^4 + 15*x^3 + 12*x^2 - 8*x

FBX|w:

x^7 - 13*x^5 - 18*x^4 + 5*x^3 + 12*x^2

FHU}w:

x^7 - 13*x^5 - 14*x^4 + 13*x^3 + 10*x^2 - 5*x

FBY~w:

x^7 - 14*x^5 - 20*x^4 + 6*x^3 + 12*x^2 - 2*x

FI\tw:

x^7 - 13*x^5 - 16*x^4 + 8*x^3 + 8*x^2

FBX~w:

x^7 - 14*x^5 - 24*x^4 - 4*x^3 + 8*x^2

FBZ~o:

x^7 - 14*x^5 - 16*x^4 + 8*x^3

FBZ~w:

x^7 - 15*x^5 - 26*x^4 - 4*x^3 + 8*x^2

F?]u_:

x^7 - 9*x^5 + 15*x^3 - 7*x

FWD[o:

x^7 - 9*x^5 - 4*x^4 + 19*x^3 + 12*x^2 - 11*x - 8

FGc}_:

x^7 - 9*x^5 - 2*x^4 + 19*x^3 + 2*x^2 - 11*x

FBj@w:

x^7 - 10*x^5 - 4*x^4 + 19*x^3 + 8*x^2 - 10*x - 4

F`YPw:

x^7 - 10*x^5 - 6*x^4 + 21*x^3 + 14*x^2 - 12*x - 8

FIe`w:

x^7 - 10*x^5 - 4*x^4 + 21*x^3 + 4*x^2 - 12*x

FIebw:

x^7 - 11*x^5 - 8*x^4 + 21*x^3 + 16*x^2 - 11*x - 8

FIefw:

x^7 - 12*x^5 - 12*x^4 + 21*x^3 + 24*x^2 - 10*x - 12

comment: This is the wheel $W_7$. It has the same characteristic polynomial as FpLYw.

FHo}g:

x^7 - 11*x^5 - 4*x^4 + 16*x^3 + 4*x^2 - 4*x

FM`hw:

x^7 - 11*x^5 - 6*x^4 + 20*x^3 + 8*x^2 - 8*x - 2

Fie`w:

x^7 - 11*x^5 - 4*x^4 + 23*x^3 - 13*x + 4

FKK}W:

x^7 - 11*x^5 - 6*x^4 + 15*x^3 + 8*x^2 - 5*x - 2

F`Lkw:

x^7 - 11*x^5 - 8*x^4 + 17*x^3 + 14*x^2 - 3*x - 2

FKL\W:

x^7 - 11*x^5 - 6*x^4 + 17*x^3 + 2*x^2 - 3*x

FY_}w:

x^7 - 12*x^5 - 8*x^4 + 19*x^3 + 8*x^2 - 8*x

comment: It has the same characteristic polynomial as FBY}o.

FKNJw:

x^7 - 12*x^5 - 10*x^4 + 16*x^3 + 12*x^2 - 3*x - 2

FKNNw:

x^7 - 13*x^5 - 14*x^4 + 15*x^3 + 16*x^2 - 3*x - 2

FHU^G:

x^7 - 11*x^5 - 6*x^4 + 24*x^3 + 8*x^2 - 16*x

FKWyw:

x^7 - 11*x^5 - 10*x^4 + 16*x^3 + 16*x^2

comment: It has the same characteristic polynomial as F_Kvw and FKcyw.

FIMmw:

x^7 - 12*x^5 - 10*x^4 + 20*x^3 + 12*x^2 - 11*x

FHd\w:

x^7 - 12*x^5 - 12*x^4 + 15*x^3 + 14*x^2 - 3*x

FKL^W:

x^7 - 12*x^5 - 10*x^4 + 18*x^3 + 10*x^2 - 4*x

FHUZw:

x^7 - 12*x^5 - 14*x^4 + 12*x^3 + 16*x^2

comment: It has the same characteristic polynomial as F_L|w.

FHU^w:

x^7 - 13*x^5 - 16*x^4 + 14*x^3 + 18*x^2 - 4*x

comment: It has the same characteristic polynomial as FG]}w.

FJQ\O:

x^7 - 10*x^5 - 2*x^4 + 20*x^3 - 9*x + 2

FHU^?:

x^7 - 10*x^5 - 4*x^4 + 24*x^3 + 8*x^2 - 16*x

Fbj@w:

x^7 - 11*x^5 - 6*x^4 + 25*x^3 + 14*x^2 - 12*x - 2

FDprW:

x^7 - 11*x^5 - 8*x^4 + 24*x^3 + 18*x^2 - 15*x - 8

FIdtW:

x^7 - 11*x^5 - 8*x^4 + 24*x^3 + 22*x^2 - 8*x - 8

FIc~G:

x^7 - 11*x^5 - 6*x^4 + 22*x^3 + 8*x^2 - 11*x

FIM\W:

x^7 - 11*x^5 - 8*x^4 + 21*x^3 + 12*x^2 - 12*x

Fh_}w:

x^7 - 12*x^5 - 10*x^4 + 23*x^3 + 20*x^2 - 9*x - 6

FSTjw:

x^7 - 12*x^5 - 12*x^4 + 18*x^3 + 20*x^2 - 5*x - 6

FDZJw:

x^7 - 12*x^5 - 12*x^4 + 20*x^3 + 22*x^2 - 8*x - 8

FIejw:

x^7 - 12*x^5 - 12*x^4 + 22*x^3 + 26*x^2 - 7*x - 8

FoL^w:

x^7 - 13*x^5 - 16*x^4 + 19*x^3 + 30*x^2 - 4*x - 10

Fbc~W:

x^7 - 13*x^5 - 12*x^4 + 19*x^3 + 16*x^2 - 4*x

FQdzw:

x^7 - 13*x^5 - 16*x^4 + 11*x^3 + 20*x^2 + 3*x - 2

FKNmw:

x^7 - 13*x^5 - 14*x^4 + 18*x^3 + 22*x^2 + x - 2

FQL}w:

x^7 - 13*x^5 - 16*x^4 + 13*x^3 + 20*x^2 - 2

FHd}w:

x^7 - 13*x^5 - 16*x^4 + 15*x^3 + 26*x^2 + 5*x - 2

FoNZw:

x^7 - 13*x^5 - 14*x^4 + 18*x^3 + 20*x^2 - 5*x - 4

FaM~w:

x^7 - 14*x^5 - 20*x^4 + 11*x^3 + 26*x^2 + 5*x - 2

FB]vW:

x^7 - 13*x^5 - 14*x^4 + 18*x^3 + 20*x^2 - 3*x - 2

FBhzw:

x^7 - 13*x^5 - 20*x^4 + 5*x^3 + 22*x^2 + 9*x

FBh|w:

x^7 - 13*x^5 - 18*x^4 + 12*x^3 + 28*x^2 + 9*x

FBh~w:

x^7 - 14*x^5 - 22*x^4 + 8*x^3 + 28*x^2 + 8*x - 2

FB]uW:

x^7 - 12*x^5 - 10*x^4 + 23*x^3 + 20*x^2 - 11*x - 8

FBY}o:

x^7 - 12*x^5 - 8*x^4 + 19*x^3 + 8*x^2 - 8*x

comment: It has the same characteristic polynomial as FY_}w.

FDp~o:

x^7 - 13*x^5 - 12*x^4 + 21*x^3 + 16*x^2 - 9*x - 4

FBh}w:

x^7 - 13*x^5 - 16*x^4 + 17*x^3 + 26*x^2 - 4*x - 8

FDpzw:

x^7 - 13*x^5 - 16*x^4 + 15*x^3 + 24*x^2 - 3*x - 8

FBj^w:

x^7 - 14*x^5 - 20*x^4 + 13*x^3 + 28*x^2 - 8

FBj~o:

x^7 - 14*x^5 - 16*x^4 + 15*x^3 + 16*x^2 - 2*x

FBj~w:

x^7 - 15*x^5 - 26*x^4 + 3*x^3 + 28*x^2 + 11*x - 2

Fo\sw:

x^7 - 12*x^5 - 4*x^4 + 12*x^3

FIU|o:

x^7 - 12*x^5 - 6*x^4 + 11*x^3 + 4*x^2 - 2*x

FBY|o:

x^7 - 12*x^5 - 8*x^4 + 12*x^3

FbY\w:

x^7 - 13*x^5 - 10*x^4 + 13*x^3 + 4*x^2 - 2*x

FImrw:

x^7 - 13*x^5 - 12*x^4 + 10*x^3 + 8*x^2

FImvw:

x^7 - 14*x^5 - 16*x^4 + 8*x^3 + 8*x^2

FQ\sw:

x^7 - 12*x^5 - 8*x^4 + 15*x^3 + 8*x^2 - 2*x

FJY[w:

x^7 - 12*x^5 - 10*x^4 + 19*x^3 + 26*x^2 + 8*x

FB\tW:

x^7 - 12*x^5 - 12*x^4 + 13*x^3 + 12*x^2

F`Lzo:

x^7 - 12*x^5 - 14*x^4 + 9*x^3 + 18*x^2 + 6*x

FXT[w:

x^7 - 12*x^5 - 10*x^4 + 19*x^3 + 12*x^2 - 8*x - 2

F@\~_:

x^7 - 12*x^5 - 12*x^4 + 11*x^3 + 14*x^2 - 2

FB]^G:

x^7 - 12*x^5 - 8*x^4 + 17*x^3 + 12*x^2 - 2*x

FJY\w:

x^7 - 13*x^5 - 14*x^4 + 16*x^3 + 22*x^2 + 6*x

F`\tw:

x^7 - 13*x^5 - 14*x^4 + 12*x^3 + 14*x^2

FJYZw:

x^7 - 13*x^5 - 18*x^4 + 6*x^3 + 18*x^2 + 6*x

FB^dw:

x^7 - 13*x^5 - 14*x^4 + 16*x^3 + 20*x^2 - 2

FJY^w:

x^7 - 14*x^5 - 20*x^4 + 9*x^3 + 24*x^2 + 8*x

FT\uW:

x^7 - 13*x^5 - 10*x^4 + 18*x^3 + 14*x^2 - 2*x

FI}vg:

x^7 - 14*x^5 - 14*x^4 + 14*x^3 + 8*x^2 - 2*x

Fdhzw:

x^7 - 14*x^5 - 16*x^4 + 9*x^3 + 10*x^2 - 2*x

FInvw:

x^7 - 15*x^5 - 22*x^4 + 5*x^3 + 14*x^2

FLh}w:

x^7 - 14*x^5 - 16*x^4 + 13*x^3 + 14*x^2

FS\zw:

x^7 - 14*x^5 - 20*x^4 + 3*x^3 + 16*x^2 + 6*x

FIm~w:

x^7 - 15*x^5 - 24*x^4 + 2*x^3 + 18*x^2 + 6*x

FIn~w:

x^7 - 16*x^5 - 30*x^4 - 7*x^3 + 14*x^2 + 6*x

FIl~g:

x^7 - 14*x^5 - 18*x^4 + 8*x^3 + 12*x^2 - 2*x

FI]|w:

x^7 - 14*x^5 - 20*x^4 + 7*x^3 + 22*x^2 + 8*x

FJY}w:

x^7 - 14*x^5 - 18*x^4 + 12*x^3 + 16*x^2

FI]~w:

x^7 - 15*x^5 - 26*x^4 - x^3 + 18*x^2 + 6*x

FI\|w:

x^7 - 14*x^5 - 24*x^4 - 3*x^3 + 14*x^2 + 6*x

FB\|w:

x^7 - 14*x^5 - 26*x^4 - 6*x^3 + 16*x^2 + 9*x

FB\~w:

x^7 - 15*x^5 - 32*x^4 - 18*x^3 + 6*x^2 + 6*x

FD\~W:

x^7 - 14*x^5 - 20*x^4 + 7*x^3 + 16*x^2 - 2

FB]~W:

x^7 - 14*x^5 - 20*x^4 + 9*x^3 + 20*x^2 + x - 2

FB]|w:

x^7 - 14*x^5 - 24*x^4 + x^3 + 24*x^2 + 12*x

FB]~w:

x^7 - 15*x^5 - 28*x^4 - 4*x^3 + 20*x^2 + 8*x - 2

FB^~w:

x^7 - 16*x^5 - 34*x^4 - 17*x^3 + 10*x^2 + 8*x

FkUhw:

x^7 - 12*x^5 - 6*x^4 + 18*x^3 - 4*x

FsLZW:

x^7 - 12*x^5 - 8*x^4 + 24*x^3 + 6*x^2 - 19*x + 6

FHU}o:

x^7 - 12*x^5 - 8*x^4 + 19*x^3 + 2*x^2 - 5*x

Fo^Pw:

x^7 - 12*x^5 - 8*x^4 + 24*x^3 + 10*x^2 - 12*x

F@]~_:

x^7 - 12*x^5 - 10*x^4 + 16*x^3 + 8*x^2 - 7*x

FA]~_:

x^7 - 12*x^5 - 8*x^4 + 19*x^3 + 6*x^2 - 8*x

comment: It has the same characteristic polynomial as Fk_zw.

FpUZw:

x^7 - 13*x^5 - 12*x^4 + 17*x^3 + 10*x^2 - 8*x

comment: It has the same characteristic polynomial as FJY}o.

Fbh\w:

x^7 - 13*x^5 - 12*x^4 + 19*x^3 + 12*x^2 - 7*x - 2

FBnbw:

x^7 - 13*x^5 - 14*x^4 + 16*x^3 + 14*x^2 - 7*x - 2

FFYmw:

x^7 - 13*x^5 - 12*x^4 + 21*x^3 + 12*x^2 - 14*x + 2

FBnfw:

x^7 - 14*x^5 - 18*x^4 + 14*x^3 + 18*x^2 - 7*x - 2

comment: It has the same characteristic polynomial as FBy}w.

FDx~g:

x^7 - 14*x^5 - 16*x^4 + 13*x^3 + 12*x^2 - 4*x

FPvZw:

x^7 - 14*x^5 - 18*x^4 + 10*x^3 + 16*x^2 - x - 2

FBnvW:

x^7 - 14*x^5 - 16*x^4 + 15*x^3 + 12*x^2 - 3*x - 2

FHu~w:

x^7 - 15*x^5 - 24*x^4 + 4*x^3 + 18*x^2 + x - 2

FBy}w:

x^7 - 14*x^5 - 18*x^4 + 14*x^3 + 18*x^2 - 7*x - 2

comment: It has the same characteristic polynomial as FBnfw.

FB]}w:

x^7 - 14*x^5 - 22*x^4 + 8*x^3 + 26*x^2 + x - 8

FBn^w:

x^7 - 15*x^5 - 26*x^4 + 3*x^3 + 24*x^2 + 2*x - 6

FBn~w:

x^7 - 16*x^5 - 32*x^4 - 10*x^3 + 16*x^2 + 7*x - 2

FF^nW:

x^7 - 15*x^5 - 20*x^4 + 4*x^3 + 8*x^2 - 2*x

FI~tw:

x^7 - 15*x^5 - 20*x^4 + 8*x^3 + 8*x^2

FB^~o:

x^7 - 15*x^5 - 24*x^4 - 2*x^3 + 8*x^2

FBn~o:

x^7 - 15*x^5 - 22*x^4 + 5*x^3 + 12*x^2 - 2*x

FB~vw:

x^7 - 16*x^5 - 28*x^4 - 6*x^3 + 8*x^2

FB~~w:

x^7 - 17*x^5 - 38*x^4 - 24*x^3 + 4*x^2 + 6*x

F@~v_:

x^7 - 13*x^5 - 6*x^4 + 6*x^3

FbY|o:

x^7 - 13*x^5 - 8*x^4 + 12*x^3

FFzbw:

x^7 - 14*x^5 - 12*x^4 + 6*x^3

FFzfw:

x^7 - 15*x^5 - 18*x^4

FK~v_:

x^7 - 14*x^5 - 12*x^4 + 13*x^3 + 12*x^2

F]p|w:

x^7 - 15*x^5 - 18*x^4 + 7*x^3 + 6*x^2

Fs\zw:

x^7 - 15*x^5 - 20*x^4 + 6*x^2

Fs\~w:

x^7 - 16*x^5 - 26*x^4 - 5*x^3 + 6*x^2

FFz~o:

x^7 - 16*x^5 - 24*x^4

FFz~w:

x^7 - 17*x^5 - 34*x^4 - 18*x^3

FF~~w:

x^7 - 18*x^5 - 44*x^4 - 39*x^3 - 12*x^2

FGeZ_:

x^7 - 9*x^5 - 6*x^4 + 19*x^3 + 24*x^2 + 5*x - 2

FJaHw:

x^7 - 10*x^5 - 8*x^4 + 21*x^3 + 32*x^2 + 12*x

F`N@w:

x^7 - 10*x^5 - 10*x^4 + 19*x^3 + 38*x^2 + 22*x + 4

FJaJw:

x^7 - 11*x^5 - 12*x^4 + 21*x^3 + 46*x^2 + 29*x + 6

FJaNw:

x^7 - 12*x^5 - 16*x^4 + 21*x^3 + 60*x^2 + 46*x + 12

FaK|W:

x^7 - 11*x^5 - 10*x^4 + 19*x^3 + 20*x^2 - 7*x - 8

FPLYw:

x^7 - 11*x^5 - 12*x^4 + 13*x^3 + 22*x^2 + 5*x - 2

FKcyw:

x^7 - 11*x^5 - 10*x^4 + 16*x^3 + 16*x^2

comment: It has the same characteristic polynomial as F_Kvw and FKWyw.

FEXlw:

x^7 - 12*x^5 - 12*x^4 + 20*x^3 + 26*x^2 - 3*x - 8

FHeZw:

x^7 - 12*x^5 - 14*x^4 + 17*x^3 + 32*x^2 + 12*x

FPTZw:

x^7 - 12*x^5 - 16*x^4 + 10*x^3 + 24*x^2 + 9*x

FKW}w:

x^7 - 12*x^5 - 12*x^4 + 20*x^3 + 28*x^2 + 5*x - 2

F`MZw:

x^7 - 12*x^5 - 14*x^4 + 13*x^3 + 22*x^2 + 4*x - 2

FPT^w:

x^7 - 13*x^5 - 18*x^4 + 14*x^3 + 34*x^2 + 12*x - 2

FJYKg:

x^7 - 10*x^5 - 6*x^4 + 24*x^3 + 22*x^2 - 7*x - 8

FJ_}W:

x^7 - 11*x^5 - 8*x^4 + 22*x^3 + 26*x^2 + 4*x - 2

FKdjg:

x^7 - 11*x^5 - 10*x^4 + 22*x^3 + 34*x^2 + 12*x

FjaHw:

x^7 - 11*x^5 - 8*x^4 + 27*x^3 + 28*x^2 - 9*x - 12

comment: This is the Moser spindle.

FKLkw:

x^7 - 11*x^5 - 10*x^4 + 21*x^3 + 30*x^2 + 9*x

F`K}W:

x^7 - 11*x^5 - 12*x^4 + 19*x^3 + 40*x^2 + 23*x + 4

FwC}w:

x^7 - 12*x^5 - 12*x^4 + 23*x^3 + 38*x^2 + 12*x - 2

FKYZw:

x^7 - 12*x^5 - 14*x^4 + 20*x^3 + 42*x^2 + 23*x + 4

F`NNw:

x^7 - 13*x^5 - 18*x^4 + 19*x^3 + 52*x^2 + 33*x + 6

F`Kyw:

x^7 - 11*x^5 - 14*x^4 + 9*x^3 + 22*x^2 + 9*x

F`K}w:

x^7 - 12*x^5 - 16*x^4 + 15*x^3 + 42*x^2 + 28*x + 6

F`Kzw:

x^7 - 12*x^5 - 20*x^4 + x^3 + 24*x^2 + 18*x + 4

F`K~w:

x^7 - 13*x^5 - 22*x^4 + 7*x^3 + 44*x^2 + 37*x + 10

FeK~W:

x^7 - 13*x^5 - 14*x^4 + 21*x^3 + 34*x^2 + 7*x - 4

FKdzw:

x^7 - 13*x^5 - 18*x^4 + 15*x^3 + 44*x^2 + 29*x + 6

FQT|w:

x^7 - 13*x^5 - 18*x^4 + 15*x^3 + 40*x^2 + 23*x + 4

F`N^W:

x^7 - 13*x^5 - 16*x^4 + 20*x^3 + 40*x^2 + 16*x

F`N^w:

x^7 - 14*x^5 - 22*x^4 + 13*x^3 + 48*x^2 + 32*x + 6

F`L~o:

x^7 - 13*x^5 - 16*x^4 + 16*x^3 + 32*x^2 + 10*x - 2

F`Lzw:

x^7 - 13*x^5 - 22*x^4 + x^3 + 26*x^2 + 19*x + 4

F`L|w:

x^7 - 13*x^5 - 20*x^4 + 6*x^3 + 26*x^2 + 12*x

F`L~w:

x^7 - 14*x^5 - 24*x^4 + 6*x^3 + 40*x^2 + 29*x + 6

F`N~o:

x^7 - 14*x^5 - 18*x^4 + 15*x^3 + 34*x^2 + 14*x

F`N~w:

x^7 - 15*x^5 - 28*x^4 + 3*x^3 + 48*x^2 + 43*x + 12

FKzPw:

x^7 - 12*x^5 - 8*x^4 + 22*x^3 + 16*x^2 - 4*x

FQT|o:

x^7 - 12*x^5 - 12*x^4 + 21*x^3 + 32*x^2 + 8*x - 2

FI]\g:

x^7 - 12*x^5 - 10*x^4 + 21*x^3 + 20*x^2 - 2

FwL[w:

x^7 - 12*x^5 - 10*x^4 + 24*x^3 + 24*x^2

FB]lg:

x^7 - 12*x^5 - 12*x^4 + 20*x^3 + 24*x^2

Fbo|w:

x^7 - 13*x^5 - 14*x^4 + 21*x^3 + 30*x^2 + 4*x - 2

FJejw:

x^7 - 13*x^5 - 16*x^4 + 18*x^3 + 34*x^2 + 12*x

FJenw:

x^7 - 14*x^5 - 20*x^4 + 16*x^3 + 40*x^2 + 16*x

Fkoxw:

x^7 - 12*x^5 - 8*x^4 + 22*x^3 + 12*x^2 - 9*x - 2

FpLYw:

x^7 - 12*x^5 - 12*x^4 + 21*x^3 + 24*x^2 - 10*x - 12

comment: It has the same characteristic polynomial as FIefw.

FkYXw:

x^7 - 12*x^5 - 10*x^4 + 26*x^3 + 24*x^2 - 12*x - 8

FPT}o:

x^7 - 12*x^5 - 10*x^4 + 21*x^3 + 14*x^2 - 11*x - 2

F`L|o:

x^7 - 12*x^5 - 14*x^4 + 16*x^3 + 24*x^2 - 3*x - 8

F`v`w:

x^7 - 12*x^5 - 10*x^4 + 26*x^3 + 28*x^2 - 7*x - 10

FpL]w:

x^7 - 13*x^5 - 14*x^4 + 21*x^3 + 26*x^2 - 7*x - 10

F`]rw:

x^7 - 13*x^5 - 16*x^4 + 16*x^3 + 24*x^2 - 4*x - 8

Fbg}w:

x^7 - 13*x^5 - 14*x^4 + 23*x^3 + 28*x^2 - 8*x - 8

F`]vw:

x^7 - 14*x^5 - 20*x^4 + 16*x^3 + 34*x^2 - x - 12

FJ]^G:

x^7 - 13*x^5 - 14*x^4 + 19*x^3 + 28*x^2 + x - 6

FL]uW:

x^7 - 13*x^5 - 12*x^4 + 24*x^3 + 22*x^2 - 9*x - 6

FJnNg:

x^7 - 14*x^5 - 16*x^4 + 18*x^3 + 24*x^2 - x - 4

FTpzw:

x^7 - 14*x^5 - 18*x^4 + 15*x^3 + 30*x^2 + 6*x - 4

FJq~w:

x^7 - 15*x^5 - 24*x^4 + 9*x^3 + 34*x^2 + 13*x - 2

FJd~W:

x^7 - 14*x^5 - 20*x^4 + 12*x^3 + 30*x^2 + 9*x - 2

FK\zw:

x^7 - 14*x^5 - 26*x^4 - 5*x^3 + 22*x^2 + 18*x + 4

FK\|w:

x^7 - 14*x^5 - 22*x^4 + 9*x^3 + 36*x^2 + 22*x + 4

F`\|w:

x^7 - 14*x^5 - 22*x^4 + 5*x^3 + 24*x^2 + 8*x - 2

FK\~w:

x^7 - 15*x^5 - 28*x^4 - x^3 + 32*x^2 + 23*x + 4

FTX}w:

x^7 - 14*x^5 - 18*x^4 + 17*x^3 + 30*x^2 + 5*x - 2

FK]~w:

x^7 - 15*x^5 - 26*x^4 + 6*x^3 + 38*x^2 + 23*x + 4

F`l~g:

x^7 - 14*x^5 - 18*x^4 + 15*x^3 + 26*x^2 + 4*x - 2

F`t|w:

x^7 - 14*x^5 - 20*x^4 + 14*x^3 + 34*x^2 + 12*x

F`]~w:

x^7 - 15*x^5 - 26*x^4 + 4*x^3 + 32*x^2 + 16*x

FK^~w:

x^7 - 16*x^5 - 32*x^4 - 5*x^3 + 34*x^2 + 28*x + 6

Ftpzw:

x^7 - 15*x^5 - 20*x^4 + 11*x^3 + 24*x^2 + 3*x - 4

FK^~o:

x^7 - 15*x^5 - 22*x^4 + 10*x^3 + 26*x^2 + 8*x

FK~vw:

x^7 - 16*x^5 - 28*x^4 + x^3 + 28*x^2 + 14*x

FK~~w:

x^7 - 17*x^5 - 38*x^4 - 17*x^3 + 28*x^2 + 33*x + 10

FJY}o:

x^7 - 13*x^5 - 12*x^4 + 17*x^3 + 10*x^2 - 8*x

comment: It has the same characteristic polynomial as FpUZw.

FJvdw:

x^7 - 14*x^5 - 16*x^4 + 20*x^3 + 20*x^2 - 11*x - 2

FLpzw:

x^7 - 14*x^5 - 20*x^4 + 10*x^3 + 22*x^2 - x - 6

FLp|w:

x^7 - 14*x^5 - 18*x^4 + 17*x^3 + 26*x^2 - 4*x - 8

Fbh|w:

x^7 - 14*x^5 - 18*x^4 + 15*x^3 + 22*x^2 - 5*x - 6

FLp~w:

x^7 - 15*x^5 - 24*x^4 + 9*x^3 + 28*x^2 - 8

FLr~o:

x^7 - 15*x^5 - 20*x^4 + 15*x^3 + 18*x^2 - 10*x

FLr~w:

x^7 - 16*x^5 - 30*x^4 + 28*x^2 + 5*x - 8

FBnvO:

x^7 - 13*x^5 - 10*x^4 + 20*x^3 + 6*x^2 - 4*x

F`]~_:

x^7 - 13*x^5 - 12*x^4 + 22*x^3 + 18*x^2 - 4*x

Fb]lg:

x^7 - 13*x^5 - 12*x^4 + 24*x^3 + 16*x^2 - 16*x

FLvbw:

x^7 - 14*x^5 - 16*x^4 + 18*x^3 + 18*x^2 - 4*x

FLvfw:

x^7 - 15*x^5 - 22*x^4 + 12*x^3 + 24*x^2

comment: It has the same characteristic polynomial as FJn^W.

FLvvO:

x^7 - 14*x^5 - 14*x^4 + 21*x^3 + 14*x^2 - 7*x - 4

Flp|w:

x^7 - 15*x^5 - 20*x^4 + 13*x^3 + 18*x^2 - 3*x - 2

FM^lw:

x^7 - 15*x^5 - 22*x^4 + 10*x^3 + 22*x^2 + x - 2

Fk]~w:

x^7 - 16*x^5 - 28*x^4 + x^3 + 22*x^2 + 5*x - 2

FJn^W:

x^7 - 15*x^5 - 22*x^4 + 12*x^3 + 24*x^2

comment: It has the same characteristic polynomial as FLvfw.

FJ]}w:

x^7 - 15*x^5 - 26*x^4 + 2*x^3 + 26*x^2 + 12*x

FJn^w:

x^7 - 16*x^5 - 30*x^4 - 2*x^3 + 26*x^2 + 12*x

Fbn~w:

x^7 - 17*x^5 - 36*x^4 - 14*x^3 + 18*x^2 + 12*x

FZn]w:

x^7 - 16*x^5 - 26*x^4 + 2*x^3 + 16*x^2 + x - 2

FLv~o:

x^7 - 16*x^5 - 26*x^4 + 4*x^3 + 16*x^2

FL~vw:

x^7 - 17*x^5 - 34*x^4 - 11*x^3 + 14*x^2 + 6*x

FL~~w:

x^7 - 18*x^5 - 44*x^4 - 32*x^3 + 6*x^2 + 15*x + 4

FU\~W:

x^7 - 15*x^5 - 22*x^4 + 8*x^3 + 20*x^2 + 2*x - 2

Fb]|w:

x^7 - 15*x^5 - 24*x^4 + 3*x^3 + 20*x^2 + 3*x - 4

FLl}w:

x^7 - 15*x^5 - 24*x^4 + 7*x^3 + 28*x^2 + 9*x - 2

FR^^w:

x^7 - 16*x^5 - 30*x^4 - 4*x^3 + 22*x^2 + 9*x - 2

FJm~w:

x^7 - 16*x^5 - 32*x^4 - 7*x^3 + 28*x^2 + 22*x + 4

FJn~w:

x^7 - 17*x^5 - 38*x^4 - 19*x^3 + 18*x^2 + 19*x + 4

FR\}w:

x^7 - 15*x^5 - 26*x^4 - 2*x^3 + 18*x^2 + 6*x - 2

FJ]|w:

x^7 - 15*x^5 - 28*x^4 - 3*x^3 + 30*x^2 + 25*x + 6

FJ]~w:

x^7 - 16*x^5 - 34*x^4 - 14*x^3 + 20*x^2 + 19*x + 4

FJ\|w:

x^7 - 15*x^5 - 32*x^4 - 17*x^3 + 12*x^2 + 15*x + 4

FJ\~w:

x^7 - 16*x^5 - 40*x^4 - 35*x^3 - 4*x^2 + 10*x + 4

FJ^~w:

x^7 - 17*x^5 - 42*x^4 - 33*x^3 + 4*x^2 + 17*x + 6

FJ~~w:

x^7 - 18*x^5 - 46*x^4 - 39*x^3 + 16*x + 6

FN~~w:

x^7 - 19*x^5 - 52*x^4 - 53*x^3 - 16*x^2 + 7*x + 4

FJn~o:

x^7 - 16*x^5 - 28*x^4 - x^3 + 18*x^2 + 6*x

FJ^~o:

x^7 - 16*x^5 - 32*x^4 - 15*x^3 + 8*x^2 + 6*x

comment: It has the same characteristic polynomial as F@~~w.

Fj]|w:

x^7 - 16*x^5 - 28*x^4 - 5*x^3 + 14*x^2 + 4*x - 2

FJ~vw:

x^7 - 17*x^5 - 36*x^4 - 18*x^3 + 10*x^2 + 8*x

Fjm~w:

x^7 - 17*x^5 - 34*x^4 - 13*x^3 + 12*x^2 + 5*x - 2

FNz~w:

x^7 - 18*x^5 - 42*x^4 - 29*x^3 + 2*x^2 + 6*x

FNz~o:

x^7 - 17*x^5 - 32*x^4 - 8*x^3 + 8*x^2

F]~vw:

x^7 - 18*x^5 - 40*x^4 - 24*x^3

F]~~w:

x^7 - 19*x^5 - 50*x^4 - 48*x^3 - 16*x^2

F^~~w:

x^7 - 20*x^5 - 60*x^4 - 75*x^3 - 44*x^2 - 10*x

F~~~w:

x^7 - 21*x^5 - 70*x^4 - 105*x^3 - 84*x^2 - 35*x - 6

comment: This is the complete graph $K_7$.

Definition

The characteristic polynomial $\phi(G,x)$ of a graph $G$ is $\det(xI-A(G))$, where $A(G)$ is the adjacency matrix. This table uses simple connected graphs named by their canonical graph6 strings [1], and $\phi(G,x)$ is a monic polynomial in $\mathbb{Z}[x]$ of degree $|V(G)|$.

Parameters

$G$

— graph (a simple connected graph, named by its canonical graph6 string)

Formulas

(1)

$\phi(G\sqcup H,x)=\phi(G,x)\phi(H,x)$ for a disjoint union of graphs.

(2)

If $G$ has $n$ vertices, $m$ edges and $t$ triangles, then $\phi(G,x)=x^n-mx^{n-2}-2t x^{n-3}+\cdots$.

(3)

$\phi(K_n,x)=(x-n+1)(x+1)^{n-1}$ for the complete graph $K_n$.

(4)

$\phi(P_n,x)=U_n(x/2)$ for the path graph $P_n$, where $U_n$ is the Chebyshev polynomial of the second kind.

(5)

$\phi(C_n,x)=2T_n(x/2)-2$ for the cycle graph $C_n$, where $T_n$ is the Chebyshev polynomial of the first kind.

Comments

(6)

Graphs are named by their graph6 string [1], McKay's compact encoding, taken after a canonical relabelling so that the name depends on the graph and not on how its vertices happen to be numbered. Recover the graph in Sage with Graph(name), and produce the name with g.canonical_label().graph6_string().

(7)

The sign convention is $\det(xI-A)$, so every polynomial is monic. MathWorld's table of characteristic polynomials [2] uses $\det(A-xI)$, which differs by a factor $(-1)^{|V(G)|}$.

(8)

The table holds connected graphs only: the characteristic polynomial of a disconnected graph is the product of those of its components, (1), so it factors into entries here.

(9)

Thirty-five of the $996$ graphs here have a name in common use, and their entries give it. The other entries are identified by their canonical graph6 strings.

(10)

Two graphs are called cospectral when they have the same characteristic polynomial. The entries for the $65$ cospectral graphs here name the other connected graphs on the same number of vertices with the same polynomial.

(11)

In Hückel molecular orbital theory [5], the $\pi$-electron energy levels of a conjugated hydrocarbon are $\alpha+\lambda\beta$, where $\lambda$ runs over the roots of the characteristic polynomial of its carbon skeleton.

Programs

(P1)

Sage

G = Graph('FjaHw')               # the Moser spindle, by its name here
G.adjacency_matrix().charpoly()

# and the name of a graph you have:
G.canonical_label().graph6_string()

Links

[1]

The graph6 and sparse6 formats (McKay)

[2]

MathWorld: Characteristic Polynomial

[3]

Wikipedia: Spectral graph theory

[4]

Brouwer: Numbers of characteristic polynomials and cospectral graphs for A

[5]

Wikipedia: Hückel method

Similar tables

Chromatic polynomials of connected graphs — the same connected graphs, named by the same canonical graph6 strings

Tutte polynomials of connected graphs — the same connected graphs, named by the same canonical graph6 strings

Chebyshev polynomials of the second kind — the path graph $P_n$ has characteristic polynomial $U_n(x/2)$

Chebyshev polynomials of the first kind — the cycle graph $C_n$ has characteristic polynomial $2T_n(x/2)-2$

$\cos(\pi x)$ for rational $x$ — the eigenvalues of the path graph $P_n$ are $2\cos(k\pi/(n+1))$ for $1\leq k\leq n$

Data properties

Entries are of type: integral polynomial

Table is complete: no (it holds every connected graph on at most $7$ vertices, all $996$ of them)

How well the digits are known: exact

How they were obtained:

An exact value, namely a polynomial with integer coefficients, so there is no precision to choose.

The generator computes $\det(xI-A(G))$ over $\mathbb{Z}[x]$ and checks the coefficients independently with Sachs' theorem, with closed forms for complete graphs, paths and cycles, and with the published counts of characteristic polynomials and cospectral graphs for all graphs on $5$, $6$ and $7$ vertices [4].