NumberDB$^\beta$ Advanced search Tags Tables Help Login
Matching-generating polynomials of connected graphs
edit · history · discussion · files · short url · statistical mechanics combinatorics polynomial
Polynomials
$G$ 
$M(G,x)$
@:
1
comment: This is the complete graph $K_1$.
A_:
x + 1
comment: This is the complete graph $K_2$.
BW:
2*x + 1
comment: This is the path $P_3$.
Bw:
3*x + 1
comment: This is the complete graph $K_3$.
CF:
3*x + 1
comment: This is the star $K_{1,3}$.
CL:
x^2 + 3*x + 1
comment: This is the path $P_4$.
CN:
x^2 + 4*x + 1
C]:
2*x^2 + 4*x + 1
comment: This is the cycle $C_4$.
C^:
2*x^2 + 5*x + 1
comment: This is the diamond graph.
C~:
3*x^2 + 6*x + 1
comment: This is the complete graph $K_4$.
D?{:
4*x + 1
comment: This is the star $K_{1,4}$.
D@s:
2*x^2 + 4*x + 1
D@{:
2*x^2 + 5*x + 1
DIk:
4*x^2 + 5*x + 1
DBk:
3*x^2 + 5*x + 1
comment: This is the bull graph.
DB{:
4*x^2 + 6*x + 1
comment: This is the dart graph.
DFw:
6*x^2 + 6*x + 1
comment: This is the complete bipartite graph $K_{2,3}$.
DF{:
6*x^2 + 7*x + 1
DBg:
3*x^2 + 4*x + 1
comment: This is the path $P_5$.
DK[:
4*x^2 + 5*x + 1
DK{:
5*x^2 + 6*x + 1
comment: This is the butterfly graph.
DLo:
5*x^2 + 5*x + 1
comment: This is the cycle $C_5$.
Dbk:
6*x^2 + 6*x + 1
comment: This is the house graph.
DL{:
7*x^2 + 7*x + 1
DJk:
5*x^2 + 6*x + 1
DJ{:
6*x^2 + 7*x + 1
DN{:
9*x^2 + 8*x + 1
comment: This is the house X graph.
DNw:
8*x^2 + 7*x + 1
D]{:
10*x^2 + 8*x + 1
comment: This is the wheel $W_5$.
D^{:
12*x^2 + 9*x + 1
D~{:
15*x^2 + 10*x + 1
comment: This is the complete graph $K_5$.
E?Bw:
5*x + 1
comment: This is the star $K_{1,5}$.
E?Fg:
3*x^2 + 5*x + 1
E?Fw:
3*x^2 + 6*x + 1
E@FG:
5*x^2 + 5*x + 1
E?NG:
4*x^2 + 5*x + 1
E@JW:
6*x^2 + 6*x + 1
E?NW:
5*x^2 + 6*x + 1
E?Nw:
6*x^2 + 7*x + 1
E?]o:
7*x^2 + 6*x + 1
E?^o:
9*x^2 + 7*x + 1
E?]w:
7*x^2 + 7*x + 1
E?^w:
9*x^2 + 8*x + 1
E?~o:
12*x^2 + 8*x + 1
comment: This is the complete bipartite graph $K_{2,4}$.
E?~w:
12*x^2 + 9*x + 1
E@QW:
x^3 + 5*x^2 + 5*x + 1
E@`w:
x^3 + 6*x^2 + 6*x + 1
E@Rw:
x^3 + 7*x^2 + 7*x + 1
E@YW:
x^3 + 7*x^2 + 6*x + 1
EHQW:
x^3 + 8*x^2 + 6*x + 1
E@UW:
x^3 + 6*x^2 + 6*x + 1
EGNW:
x^3 + 9*x^2 + 7*x + 1
EAMw:
x^3 + 8*x^2 + 7*x + 1
E@Vw:
x^3 + 10*x^2 + 8*x + 1
E@YO:
x^3 + 6*x^2 + 5*x + 1
comment: This is the path $P_6$.
EI_w:
2*x^3 + 8*x^2 + 6*x + 1
EGdo:
x^3 + 8*x^2 + 6*x + 1
EGcw:
x^3 + 7*x^2 + 6*x + 1
E@ow:
7*x^2 + 6*x + 1
EK`w:
2*x^3 + 10*x^2 + 7*x + 1
ECXw:
2*x^3 + 9*x^2 + 7*x + 1
EGdw:
x^3 + 9*x^2 + 7*x + 1
E_Nw:
2*x^3 + 11*x^2 + 8*x + 1
E@NW:
8*x^2 + 7*x + 1
E@Nw:
9*x^2 + 8*x + 1
E_]o:
2*x^3 + 11*x^2 + 7*x + 1
EENg:
2*x^3 + 13*x^2 + 8*x + 1
EC\w:
2*x^3 + 11*x^2 + 8*x + 1
E@^W:
x^3 + 11*x^2 + 8*x + 1
E_]w:
2*x^3 + 12*x^2 + 8*x + 1
E@vw:
2*x^3 + 14*x^2 + 9*x + 1
E@^o:
x^3 + 12*x^2 + 8*x + 1
E@]w:
x^3 + 10*x^2 + 8*x + 1
E@^w:
x^3 + 13*x^2 + 9*x + 1
E@~o:
2*x^3 + 16*x^2 + 9*x + 1
E@~w:
2*x^3 + 17*x^2 + 10*x + 1
EBYW:
2*x^3 + 10*x^2 + 7*x + 1
EBYw:
2*x^3 + 12*x^2 + 8*x + 1
EBZw:
2*x^3 + 14*x^2 + 9*x + 1
EIe_:
2*x^3 + 9*x^2 + 6*x + 1
comment: This is the cycle $C_6$.
EKNG:
3*x^3 + 11*x^2 + 7*x + 1
EHUW:
2*x^3 + 10*x^2 + 7*x + 1
EoLW:
2*x^3 + 11*x^2 + 7*x + 1
E@]o:
x^3 + 9*x^2 + 7*x + 1
EA]o:
x^3 + 10*x^2 + 7*x + 1
EaMw:
3*x^3 + 13*x^2 + 8*x + 1
EBhw:
2*x^3 + 12*x^2 + 8*x + 1
EBjW:
2*x^3 + 13*x^2 + 8*x + 1
EBjw:
3*x^3 + 15*x^2 + 9*x + 1
EImo:
4*x^3 + 14*x^2 + 8*x + 1
EJYW:
2*x^3 + 13*x^2 + 8*x + 1
EIno:
4*x^3 + 17*x^2 + 9*x + 1
EImw:
4*x^3 + 16*x^2 + 9*x + 1
EInw:
4*x^3 + 19*x^2 + 10*x + 1
EI]w:
2*x^3 + 15*x^2 + 9*x + 1
EB]w:
2*x^3 + 14*x^2 + 9*x + 1
EB^w:
2*x^3 + 17*x^2 + 10*x + 1
EHuw:
3*x^3 + 16*x^2 + 9*x + 1
EBnW:
2*x^3 + 15*x^2 + 9*x + 1
EBnw:
3*x^3 + 18*x^2 + 10*x + 1
EB~w:
4*x^3 + 22*x^2 + 11*x + 1
EFz_:
6*x^3 + 18*x^2 + 9*x + 1
comment: This is the complete bipartite graph $K_{3,3}$.
Es\w:
6*x^3 + 21*x^2 + 10*x + 1
EB~o:
4*x^3 + 20*x^2 + 10*x + 1
EFzw:
6*x^3 + 24*x^2 + 11*x + 1
EF~w:
6*x^3 + 27*x^2 + 12*x + 1
EPTW:
2*x^3 + 10*x^2 + 7*x + 1
E`NG:
x^3 + 11*x^2 + 7*x + 1
E`NW:
2*x^3 + 13*x^2 + 8*x + 1
E`Lw:
3*x^3 + 12*x^2 + 8*x + 1
E`Nw:
3*x^3 + 15*x^2 + 9*x + 1
EJeg:
2*x^3 + 14*x^2 + 8*x + 1
EJqw:
3*x^3 + 17*x^2 + 9*x + 1
EK\w:
3*x^3 + 15*x^2 + 9*x + 1
EK]w:
3*x^3 + 16*x^2 + 9*x + 1
E`]w:
4*x^3 + 16*x^2 + 9*x + 1
EK^w:
4*x^3 + 19*x^2 + 10*x + 1
EK~o:
4*x^3 + 21*x^2 + 10*x + 1
EK~w:
5*x^3 + 23*x^2 + 11*x + 1
EBn_:
3*x^3 + 14*x^2 + 8*x + 1
E`]o:
3*x^3 + 14*x^2 + 8*x + 1
ELpw:
4*x^3 + 17*x^2 + 9*x + 1
ELrw:
5*x^3 + 20*x^2 + 10*x + 1
comment: This is the wheel $W_6$.
ELv_:
4*x^3 + 18*x^2 + 9*x + 1
Ek]w:
5*x^3 + 21*x^2 + 10*x + 1
EJnW:
4*x^3 + 20*x^2 + 10*x + 1
Ebnw:
6*x^3 + 24*x^2 + 11*x + 1
EL~w:
7*x^3 + 28*x^2 + 12*x + 1
ER^W:
5*x^3 + 20*x^2 + 10*x + 1
EJmw:
4*x^3 + 19*x^2 + 10*x + 1
EJnw:
5*x^3 + 23*x^2 + 11*x + 1
EJ]w:
3*x^3 + 18*x^2 + 10*x + 1
EJ^w:
3*x^3 + 21*x^2 + 11*x + 1
EJ~w:
6*x^3 + 27*x^2 + 12*x + 1
EN~w:
9*x^3 + 33*x^2 + 13*x + 1
EL~o:
6*x^3 + 25*x^2 + 11*x + 1
EJ~o:
6*x^3 + 24*x^2 + 11*x + 1
Ejmw:
7*x^3 + 25*x^2 + 11*x + 1
ENzw:
8*x^3 + 29*x^2 + 12*x + 1
E]~o:
8*x^3 + 30*x^2 + 12*x + 1
E]~w:
10*x^3 + 34*x^2 + 13*x + 1
E^~w:
12*x^3 + 39*x^2 + 14*x + 1
E~~w:
15*x^3 + 45*x^2 + 15*x + 1
comment: This is the complete graph $K_6$.
F??Fw:
6*x + 1
comment: This is the star $K_{1,6}$.
F??Ng:
4*x^2 + 6*x + 1
F??Nw:
4*x^2 + 7*x + 1
F?CNG:
7*x^2 + 6*x + 1
F??^G:
6*x^2 + 6*x + 1
F??^o:
8*x^2 + 7*x + 1
F??^W:
7*x^2 + 7*x + 1
F??^w:
8*x^2 + 8*x + 1
F??}O:
8*x^2 + 6*x + 1
F??}o:
10*x^2 + 7*x + 1
F??}W:
8*x^2 + 7*x + 1
F??~o:
12*x^2 + 8*x + 1
F??}w:
10*x^2 + 8*x + 1
F??~w:
12*x^2 + 9*x + 1
F?@|o:
13*x^2 + 8*x + 1
F?@~o:
16*x^2 + 9*x + 1
F?@|w:
13*x^2 + 9*x + 1
F?@~w:
16*x^2 + 10*x + 1
F?B~o:
20*x^2 + 10*x + 1
comment: This is the complete bipartite graph $K_{2,5}$.
F?B~w:
20*x^2 + 11*x + 1
F?CeW:
2*x^3 + 7*x^2 + 6*x + 1
F@?Mw:
2*x^3 + 8*x^2 + 7*x + 1
F?Cfw:
2*x^3 + 9*x^2 + 8*x + 1
F@?]O:
2*x^3 + 9*x^2 + 6*x + 1
F?Cmg:
2*x^3 + 10*x^2 + 7*x + 1
F@?]W:
2*x^3 + 10*x^2 + 7*x + 1
F@CeW:
2*x^3 + 11*x^2 + 7*x + 1
F?CmW:
2*x^3 + 9*x^2 + 7*x + 1
F@?^W:
2*x^3 + 12*x^2 + 8*x + 1
F?G]w:
2*x^3 + 11*x^2 + 8*x + 1
F?Cnw:
2*x^3 + 13*x^2 + 9*x + 1
F@OKg:
3*x^3 + 9*x^2 + 6*x + 1
F?DcW:
2*x^3 + 8*x^2 + 6*x + 1
F@IAw:
4*x^3 + 11*x^2 + 7*x + 1
F@AJo:
3*x^3 + 11*x^2 + 7*x + 1
F@@Kw:
3*x^3 + 10*x^2 + 7*x + 1
F?Dcw:
2*x^3 + 10*x^2 + 7*x + 1
F@PDw:
4*x^3 + 13*x^2 + 8*x + 1
F?_rw:
4*x^3 + 12*x^2 + 8*x + 1
F@@Lw:
3*x^3 + 12*x^2 + 8*x + 1
FG?^w:
4*x^3 + 14*x^2 + 9*x + 1
F?C^G:
10*x^2 + 7*x + 1
F?C^W:
11*x^2 + 8*x + 1
F?C^w:
12*x^2 + 9*x + 1
F@@ko:
3*x^3 + 12*x^2 + 7*x + 1
F?O|o:
4*x^3 + 14*x^2 + 8*x + 1
F?W\g:
3*x^3 + 14*x^2 + 8*x + 1
FG?}o:
4*x^3 + 15*x^2 + 8*x + 1
F?H[w:
3*x^3 + 12*x^2 + 8*x + 1
F?Dkw:
2*x^3 + 12*x^2 + 8*x + 1
F@@kw:
3*x^3 + 13*x^2 + 8*x + 1
F?W^g:
4*x^3 + 17*x^2 + 9*x + 1
F?O|w:
4*x^3 + 15*x^2 + 9*x + 1
F?Dlw:
3*x^3 + 15*x^2 + 9*x + 1
FG?}w:
4*x^3 + 16*x^2 + 9*x + 1
F?Dnw:
4*x^3 + 18*x^2 + 10*x + 1
F?O|_:
4*x^3 + 12*x^2 + 7*x + 1
F@?}O:
2*x^3 + 12*x^2 + 7*x + 1
F?`ro:
6*x^3 + 15*x^2 + 8*x + 1
FGAZo:
4*x^3 + 15*x^2 + 8*x + 1
F?O|g:
4*x^3 + 13*x^2 + 8*x + 1
F@?}W:
2*x^3 + 13*x^2 + 8*x + 1
F_?~o:
6*x^3 + 18*x^2 + 9*x + 1
F?`rw:
6*x^3 + 16*x^2 + 9*x + 1
FGAZw:
4*x^3 + 16*x^2 + 9*x + 1
F_?~w:
6*x^3 + 19*x^2 + 10*x + 1
F?C~O:
2*x^3 + 14*x^2 + 8*x + 1
F@C]W:
2*x^3 + 13*x^2 + 8*x + 1
F?C~o:
2*x^3 + 16*x^2 + 9*x + 1
F?C~W:
2*x^3 + 15*x^2 + 9*x + 1
F?C}w:
2*x^3 + 14*x^2 + 9*x + 1
F?C~w:
2*x^3 + 17*x^2 + 10*x + 1
F?`zo:
6*x^3 + 18*x^2 + 9*x + 1
F?D~O:
4*x^3 + 18*x^2 + 9*x + 1
F_@|o:
6*x^3 + 19*x^2 + 9*x + 1
F?Fno:
6*x^3 + 22*x^2 + 10*x + 1
F?`zw:
6*x^3 + 19*x^2 + 10*x + 1
F?D~W:
4*x^3 + 19*x^2 + 10*x + 1
F_@|w:
6*x^3 + 20*x^2 + 10*x + 1
F?Fnw:
6*x^3 + 23*x^2 + 11*x + 1
F?D|o:
3*x^3 + 17*x^2 + 9*x + 1
F?D~o:
4*x^3 + 21*x^2 + 10*x + 1
F?D|w:
3*x^3 + 18*x^2 + 10*x + 1
F?D~w:
4*x^3 + 22*x^2 + 11*x + 1
F?F~o:
6*x^3 + 26*x^2 + 11*x + 1
F?F~w:
6*x^3 + 27*x^2 + 12*x + 1
F?KuW:
4*x^3 + 14*x^2 + 8*x + 1
F@CmW:
4*x^3 + 14*x^2 + 8*x + 1
F?Kuw:
4*x^3 + 16*x^2 + 9*x + 1
F?Kvw:
4*x^3 + 18*x^2 + 10*x + 1
FICcW:
5*x^3 + 13*x^2 + 7*x + 1
F@HSW:
4*x^3 + 12*x^2 + 7*x + 1
F?_yo:
3*x^3 + 11*x^2 + 7*x + 1
F@O^G:
6*x^3 + 15*x^2 + 8*x + 1
FGG[w:
5*x^3 + 14*x^2 + 8*x + 1
F@Okw:
5*x^3 + 14*x^2 + 8*x + 1
FI?\W:
5*x^3 + 15*x^2 + 8*x + 1
F@O[w:
4*x^3 + 13*x^2 + 8*x + 1
F?StW:
4*x^3 + 14*x^2 + 8*x + 1
FGG]w:
6*x^3 + 17*x^2 + 9*x + 1
F?MRw:
5*x^3 + 16*x^2 + 9*x + 1
F?LVW:
5*x^3 + 17*x^2 + 9*x + 1
F?LVw:
6*x^3 + 19*x^2 + 10*x + 1
FIAHo:
6*x^3 + 13*x^2 + 7*x + 1
F?StG:
4*x^3 + 12*x^2 + 7*x + 1
F@G]G:
4*x^3 + 12*x^2 + 7*x + 1
F?oow:
2*x^3 + 11*x^2 + 7*x + 1
FIa@w:
8*x^3 + 16*x^2 + 8*x + 1
F?org:
6*x^3 + 15*x^2 + 8*x + 1
FIAHw:
6*x^3 + 15*x^2 + 8*x + 1
F?opw:
4*x^3 + 14*x^2 + 8*x + 1
F?YPw:
4*x^3 + 14*x^2 + 8*x + 1
Fo?Zw:
8*x^3 + 18*x^2 + 9*x + 1
F?NBw:
6*x^3 + 17*x^2 + 9*x + 1
F?NFw:
8*x^3 + 20*x^2 + 10*x + 1
F@H[o:
6*x^3 + 15*x^2 + 8*x + 1
F@TTW:
8*x^3 + 19*x^2 + 9*x + 1
F@IZo:
6*x^3 + 18*x^2 + 9*x + 1
F?Tto:
7*x^3 + 19*x^2 + 9*x + 1
F@H[w:
6*x^3 + 17*x^2 + 9*x + 1
F@H^o:
8*x^3 + 22*x^2 + 10*x + 1
F@H]w:
8*x^3 + 21*x^2 + 10*x + 1
F@H\w:
6*x^3 + 20*x^2 + 10*x + 1
F@Dmw:
7*x^3 + 21*x^2 + 10*x + 1
F@H^w:
8*x^3 + 24*x^2 + 11*x + 1
Fo?yo:
8*x^3 + 17*x^2 + 8*x + 1
F?L^?:
5*x^3 + 16*x^2 + 8*x + 1
F?[uG:
6*x^3 + 16*x^2 + 8*x + 1
F_LLg:
10*x^3 + 20*x^2 + 9*x + 1
F?Uro:
7*x^3 + 19*x^2 + 9*x + 1
F?]Rg:
8*x^3 + 19*x^2 + 9*x + 1
F?svG:
8*x^3 + 20*x^2 + 9*x + 1
FADlW:
7*x^3 + 18*x^2 + 9*x + 1
FCDjW:
8*x^3 + 18*x^2 + 9*x + 1
Fo?yw:
8*x^3 + 19*x^2 + 9*x + 1
F?NPw:
4*x^3 + 17*x^2 + 9*x + 1
FEG^W:
10*x^3 + 23*x^2 + 10*x + 1
FCDnW:
10*x^3 + 22*x^2 + 10*x + 1
F@FJw:
7*x^3 + 21*x^2 + 10*x + 1
F?drw:
8*x^3 + 21*x^2 + 10*x + 1
F?NVW:
8*x^3 + 22*x^2 + 10*x + 1
F@FNw:
10*x^3 + 25*x^2 + 11*x + 1
F@KuW:
4*x^3 + 18*x^2 + 9*x + 1
F@G}w:
4*x^3 + 20*x^2 + 10*x + 1
F?K}w:
4*x^3 + 19*x^2 + 10*x + 1
F?K~w:
4*x^3 + 22*x^2 + 11*x + 1
F?L^_:
6*x^3 + 19*x^2 + 9*x + 1
FAEhw:
5*x^3 + 17*x^2 + 9*x + 1
F?L\g:
5*x^3 + 17*x^2 + 9*x + 1
F?L^G:
5*x^3 + 18*x^2 + 9*x + 1
F?L[w:
4*x^3 + 15*x^2 + 9*x + 1
F@D^W:
6*x^3 + 21*x^2 + 10*x + 1
F?S|w:
5*x^3 + 19*x^2 + 10*x + 1
F?L^W:
5*x^3 + 20*x^2 + 10*x + 1
F?L^w:
6*x^3 + 23*x^2 + 11*x + 1
F?NN_:
8*x^3 + 20*x^2 + 9*x + 1
F?drW:
6*x^3 + 18*x^2 + 9*x + 1
F?LuW:
6*x^3 + 18*x^2 + 9*x + 1
F?K}W:
4*x^3 + 16*x^2 + 9*x + 1
F?Lkw:
4*x^3 + 16*x^2 + 9*x + 1
F?NNg:
8*x^3 + 22*x^2 + 10*x + 1
F?NJw:
6*x^3 + 20*x^2 + 10*x + 1
F?NNw:
8*x^3 + 24*x^2 + 11*x + 1
F@J]o:
12*x^3 + 24*x^2 + 10*x + 1
F@J^o:
12*x^3 + 28*x^2 + 11*x + 1
F@J]w:
12*x^3 + 26*x^2 + 11*x + 1
F@J^w:
12*x^3 + 30*x^2 + 12*x + 1
F@H}o:
8*x^3 + 23*x^2 + 10*x + 1
F?L~o:
8*x^3 + 26*x^2 + 11*x + 1
F@H}w:
8*x^3 + 25*x^2 + 11*x + 1
F?L|w:
6*x^3 + 23*x^2 + 11*x + 1
F?L~w:
8*x^3 + 28*x^2 + 12*x + 1
F@Fmo:
10*x^3 + 24*x^2 + 10*x + 1
F?s~g:
10*x^3 + 27*x^2 + 11*x + 1
F@Fmw:
10*x^3 + 26*x^2 + 11*x + 1
F?L}w:
7*x^3 + 24*x^2 + 11*x + 1
F?dzw:
8*x^3 + 24*x^2 + 11*x + 1
F?N^W:
8*x^3 + 25*x^2 + 11*x + 1
F?N^w:
10*x^3 + 29*x^2 + 12*x + 1
F?N~o:
12*x^3 + 32*x^2 + 12*x + 1
F?N~w:
12*x^3 + 34*x^2 + 13*x + 1
FBXcw:
12*x^3 + 24*x^2 + 10*x + 1
F?\sw:
8*x^3 + 22*x^2 + 10*x + 1
FIO|w:
12*x^3 + 27*x^2 + 11*x + 1
F?\tw:
10*x^3 + 26*x^2 + 11*x + 1
F?\vw:
12*x^3 + 30*x^2 + 12*x + 1
F?]v_:
14*x^3 + 25*x^2 + 10*x + 1
F?lrg:
10*x^3 + 23*x^2 + 10*x + 1
F?\tg:
10*x^3 + 23*x^2 + 10*x + 1
FBEmW:
11*x^3 + 24*x^2 + 10*x + 1
F?L|o:
6*x^3 + 21*x^2 + 10*x + 1
F?T|o:
7*x^3 + 22*x^2 + 10*x + 1
F?v`w:
8*x^3 + 23*x^2 + 10*x + 1
F?lvg:
14*x^3 + 28*x^2 + 11*x + 1
F?]rw:
10*x^3 + 26*x^2 + 11*x + 1
F?]uw:
11*x^3 + 27*x^2 + 11*x + 1
F?]vw:
14*x^3 + 31*x^2 + 12*x + 1
FIQ|o:
18*x^3 + 30*x^2 + 11*x + 1
F?\~_:
12*x^3 + 28*x^2 + 11*x + 1
F?]~_:
14*x^3 + 29*x^2 + 11*x + 1
F?^vo:
18*x^3 + 34*x^2 + 12*x + 1
FIQ|w:
18*x^3 + 33*x^2 + 12*x + 1
F?^vw:
18*x^3 + 37*x^2 + 13*x + 1
F?\~g:
12*x^3 + 31*x^2 + 12*x + 1
F?\|w:
10*x^3 + 29*x^2 + 12*x + 1
F?\~w:
12*x^3 + 34*x^2 + 13*x + 1
F?^tw:
14*x^3 + 32*x^2 + 12*x + 1
F?]}w:
11*x^3 + 30*x^2 + 12*x + 1
F?]~w:
14*x^3 + 35*x^2 + 13*x + 1
F?^~w:
18*x^3 + 41*x^2 + 14*x + 1
F?~v_:
24*x^3 + 36*x^2 + 12*x + 1
comment: This is the complete bipartite graph $K_{3,4}$.
F?~vg:
24*x^3 + 40*x^2 + 13*x + 1
F?^~o:
18*x^3 + 38*x^2 + 13*x + 1
F?~vw:
24*x^3 + 44*x^2 + 14*x + 1
F?~~w:
24*x^3 + 48*x^2 + 15*x + 1
F@Q?w:
4*x^3 + 9*x^2 + 6*x + 1
F@Q@w:
5*x^3 + 11*x^2 + 7*x + 1
F@QBw:
6*x^3 + 13*x^2 + 8*x + 1
F@QFw:
7*x^3 + 15*x^2 + 9*x + 1
F@HSO:
4*x^3 + 10*x^2 + 6*x + 1
comment: This is the path $P_7$.
F@O\G:
5*x^3 + 12*x^2 + 7*x + 1
FA_pW:
5*x^3 + 12*x^2 + 7*x + 1
FHQ?w:
6*x^3 + 13*x^2 + 7*x + 1
F@OsW:
4*x^3 + 12*x^2 + 7*x + 1
F@R@o:
5*x^3 + 13*x^2 + 7*x + 1
F@QGw:
4*x^3 + 11*x^2 + 7*x + 1
FG_qw:
7*x^3 + 15*x^2 + 8*x + 1
FGEJg:
6*x^3 + 15*x^2 + 8*x + 1
FG_Zg:
6*x^3 + 15*x^2 + 8*x + 1
F`Q@w:
7*x^3 + 16*x^2 + 8*x + 1
FA_hw:
6*x^3 + 14*x^2 + 8*x + 1
F@QHw:
5*x^3 + 14*x^2 + 8*x + 1
F`?^W:
8*x^3 + 18*x^2 + 9*x + 1
FCHJw:
8*x^3 + 17*x^2 + 9*x + 1
FGEJw:
7*x^3 + 17*x^2 + 9*x + 1
F_Cnw:
9*x^3 + 20*x^2 + 10*x + 1
FGC\W:
5*x^3 + 14*x^2 + 8*x + 1
FGC^G:
4*x^3 + 15*x^2 + 8*x + 1
FGC^W:
5*x^3 + 17*x^2 + 9*x + 1
FGC\w:
6*x^3 + 16*x^2 + 9*x + 1
FGC^w:
6*x^3 + 19*x^2 + 10*x + 1
FK?}O:
8*x^3 + 17*x^2 + 8*x + 1
FAMRW:
8*x^3 + 19*x^2 + 9*x + 1
F@QZo:
7*x^3 + 19*x^2 + 9*x + 1
F_W\g:
9*x^3 + 20*x^2 + 9*x + 1
FA_xw:
7*x^3 + 17*x^2 + 9*x + 1
FAIXw:
6*x^3 + 17*x^2 + 9*x + 1
FCHiw:
8*x^3 + 18*x^2 + 9*x + 1
FG_yw:
8*x^3 + 18*x^2 + 9*x + 1
FGC}W:
7*x^3 + 18*x^2 + 9*x + 1
FK?}W:
9*x^3 + 19*x^2 + 9*x + 1
FA_~o:
10*x^3 + 23*x^2 + 10*x + 1
F@`Zw:
9*x^3 + 21*x^2 + 10*x + 1
F@QZw:
8*x^3 + 21*x^2 + 10*x + 1
F_Dlw:
10*x^3 + 22*x^2 + 10*x + 1
F@Q^w:
11*x^3 + 25*x^2 + 11*x + 1
F@LSW:
5*x^3 + 15*x^2 + 8*x + 1
F@Maw:
6*x^3 + 18*x^2 + 9*x + 1
FAStW:
6*x^3 + 19*x^2 + 9*x + 1
FGD\o:
7*x^3 + 19*x^2 + 9*x + 1
F@Lew:
7*x^3 + 22*x^2 + 10*x + 1
F@_zw:
7*x^3 + 20*x^2 + 10*x + 1
FAG}w:
7*x^3 + 21*x^2 + 10*x + 1
FGC}w:
8*x^3 + 21*x^2 + 10*x + 1
F@O~w:
8*x^3 + 24*x^2 + 11*x + 1
F`?}O:
6*x^3 + 17*x^2 + 8*x + 1
FODZo:
9*x^3 + 19*x^2 + 9*x + 1
F_K^G:
8*x^3 + 20*x^2 + 9*x + 1
FGEZo:
7*x^3 + 19*x^2 + 9*x + 1
FGEXw:
7*x^3 + 17*x^2 + 9*x + 1
FGDkw:
6*x^3 + 18*x^2 + 9*x + 1
F`?}W:
7*x^3 + 19*x^2 + 9*x + 1
F`C^W:
10*x^3 + 23*x^2 + 10*x + 1
FODZw:
10*x^3 + 21*x^2 + 10*x + 1
F_C~W:
9*x^3 + 22*x^2 + 10*x + 1
FGEZw:
8*x^3 + 21*x^2 + 10*x + 1
F_C~w:
11*x^3 + 25*x^2 + 11*x + 1
F@`zo:
10*x^3 + 23*x^2 + 10*x + 1
F@Q}o:
10*x^3 + 24*x^2 + 10*x + 1
F@P|o:
8*x^3 + 23*x^2 + 10*x + 1
F_D|o:
11*x^3 + 24*x^2 + 10*x + 1
F@`~o:
12*x^3 + 28*x^2 + 11*x + 1
F@`zw:
11*x^3 + 25*x^2 + 11*x + 1
F@Q}w:
11*x^3 + 26*x^2 + 11*x + 1
F@P|w:
9*x^3 + 25*x^2 + 11*x + 1
F_D|w:
12*x^3 + 26*x^2 + 11*x + 1
F@`~w:
13*x^3 + 30*x^2 + 12*x + 1
F@P~o:
9*x^3 + 27*x^2 + 11*x + 1
F@P~w:
10*x^3 + 29*x^2 + 12*x + 1
F@R~o:
14*x^3 + 33*x^2 + 12*x + 1
F@R~w:
15*x^3 + 35*x^2 + 13*x + 1
FHQSO:
7*x^3 + 14*x^2 + 7*x + 1
comment: This is the cycle $C_7$.
FGSkg:
7*x^3 + 16*x^2 + 8*x + 1
FCXPW:
7*x^3 + 16*x^2 + 8*x + 1
Fk?gw:
8*x^3 + 17*x^2 + 8*x + 1
FK_qW:
9*x^3 + 17*x^2 + 8*x + 1
FGC{o:
6*x^3 + 15*x^2 + 8*x + 1
FICkW:
7*x^3 + 16*x^2 + 8*x + 1
FKHGw:
8*x^3 + 16*x^2 + 8*x + 1
F?L\_:
5*x^3 + 15*x^2 + 8*x + 1
FGK]G:
6*x^3 + 16*x^2 + 8*x + 1
F_StW:
10*x^3 + 20*x^2 + 9*x + 1
FGUPw:
9*x^3 + 19*x^2 + 9*x + 1
FOLQw:
9*x^3 + 19*x^2 + 9*x + 1
FoCiw:
10*x^3 + 20*x^2 + 9*x + 1
FKG]W:
11*x^3 + 20*x^2 + 9*x + 1
FAN@w:
8*x^3 + 19*x^2 + 9*x + 1
FAYPw:
8*x^3 + 19*x^2 + 9*x + 1
F_YPw:
9*x^3 + 20*x^2 + 9*x + 1
F@YPw:
7*x^3 + 18*x^2 + 9*x + 1
FaG\w:
12*x^3 + 23*x^2 + 10*x + 1
FB_mw:
11*x^3 + 23*x^2 + 10*x + 1
F@YRw:
10*x^3 + 22*x^2 + 10*x + 1
F@YVw:
13*x^3 + 26*x^2 + 11*x + 1
FGLSW:
7*x^3 + 16*x^2 + 8*x + 1
F@Tcw:
8*x^3 + 19*x^2 + 9*x + 1
FGLSw:
8*x^3 + 19*x^2 + 9*x + 1
F@Tdw:
9*x^3 + 22*x^2 + 10*x + 1
F@Tfw:
10*x^3 + 25*x^2 + 11*x + 1
F@Umg:
12*x^3 + 24*x^2 + 10*x + 1
F@Xsw:
10*x^3 + 23*x^2 + 10*x + 1
F@hqw:
10*x^3 + 23*x^2 + 10*x + 1
FBJKw:
12*x^3 + 24*x^2 + 10*x + 1
F@Y^_:
13*x^3 + 25*x^2 + 10*x + 1
F@Lkw:
7*x^3 + 21*x^2 + 10*x + 1
F@h^g:
14*x^3 + 28*x^2 + 11*x + 1
F@Y]w:
13*x^3 + 27*x^2 + 11*x + 1
F@Ujw:
11*x^3 + 26*x^2 + 11*x + 1
F@Y^w:
15*x^3 + 31*x^2 + 12*x + 1
FHTcw:
10*x^3 + 24*x^2 + 10*x + 1
F@Tkw:
9*x^3 + 22*x^2 + 10*x + 1
FHO}w:
11*x^3 + 27*x^2 + 11*x + 1
FALlw:
11*x^3 + 26*x^2 + 11*x + 1
F@Tlw:
10*x^3 + 26*x^2 + 11*x + 1
FGL^w:
12*x^3 + 30*x^2 + 12*x + 1
FAdl_:
11*x^3 + 21*x^2 + 9*x + 1
F@U^?:
10*x^3 + 21*x^2 + 9*x + 1
FBebW:
14*x^3 + 25*x^2 + 10*x + 1
F@fbo:
13*x^3 + 25*x^2 + 10*x + 1
FHQZo:
11*x^3 + 24*x^2 + 10*x + 1
FBO|W:
10*x^3 + 23*x^2 + 10*x + 1
FHQ[w:
13*x^3 + 24*x^2 + 10*x + 1
FHQ^o:
16*x^3 + 29*x^2 + 11*x + 1
FD`jw:
15*x^3 + 28*x^2 + 11*x + 1
F@jRw:
14*x^3 + 28*x^2 + 11*x + 1
FHQZw:
12*x^3 + 27*x^2 + 11*x + 1
FHQ^w:
17*x^3 + 32*x^2 + 12*x + 1
F@W}g:
9*x^3 + 23*x^2 + 10*x + 1
F@L[w:
7*x^3 + 20*x^2 + 10*x + 1
F@T\W:
9*x^3 + 22*x^2 + 10*x + 1
F@Lmw:
9*x^3 + 26*x^2 + 11*x + 1
F@MZw:
8*x^3 + 24*x^2 + 11*x + 1
FAS|w:
9*x^3 + 25*x^2 + 11*x + 1
FAK~W:
10*x^3 + 26*x^2 + 11*x + 1
F@L^w:
10*x^3 + 29*x^2 + 12*x + 1
F@Vcw:
11*x^3 + 24*x^2 + 10*x + 1
F@U^W:
12*x^3 + 27*x^2 + 11*x + 1
F@UZw:
10*x^3 + 25*x^2 + 11*x + 1
F@U^w:
13*x^3 + 30*x^2 + 12*x + 1
FHQ}o:
16*x^3 + 30*x^2 + 11*x + 1
FGN^o:
18*x^3 + 34*x^2 + 12*x + 1
FGU|w:
17*x^3 + 32*x^2 + 12*x + 1
FGL}w:
13*x^3 + 31*x^2 + 12*x + 1
FHQ}w:
17*x^3 + 33*x^2 + 12*x + 1
FGN^w:
19*x^3 + 37*x^2 + 13*x + 1
F@d~o:
16*x^3 + 33*x^2 + 12*x + 1
F@Vlw:
15*x^3 + 32*x^2 + 12*x + 1
F@dzw:
13*x^3 + 30*x^2 + 12*x + 1
F@T|w:
12*x^3 + 30*x^2 + 12*x + 1
F@U}w:
14*x^3 + 31*x^2 + 12*x + 1
FGN\w:
16*x^3 + 32*x^2 + 12*x + 1
FAM~w:
17*x^3 + 36*x^2 + 13*x + 1
F@T~o:
13*x^3 + 32*x^2 + 12*x + 1
F@T~w:
14*x^3 + 35*x^2 + 13*x + 1
F@V~o:
20*x^3 + 39*x^2 + 13*x + 1
F@V~w:
21*x^3 + 42*x^2 + 14*x + 1
FCX_w:
8*x^3 + 16*x^2 + 8*x + 1
FK`_w:
8*x^3 + 17*x^2 + 8*x + 1
F_KuW:
10*x^3 + 20*x^2 + 9*x + 1
FOTPw:
10*x^3 + 19*x^2 + 9*x + 1
F`CmW:
10*x^3 + 20*x^2 + 9*x + 1
F`G]w:
12*x^3 + 23*x^2 + 10*x + 1
F_Krw:
12*x^3 + 22*x^2 + 10*x + 1
F_Kvw:
14*x^3 + 26*x^2 + 11*x + 1
F?\t_:
10*x^3 + 20*x^2 + 9*x + 1
FK_yo:
12*x^3 + 21*x^2 + 9*x + 1
F@\cg:
9*x^3 + 20*x^2 + 9*x + 1
F`KqW:
10*x^3 + 20*x^2 + 9*x + 1
FCdj_:
10*x^3 + 21*x^2 + 9*x + 1
FDhaw:
14*x^3 + 25*x^2 + 10*x + 1
FBZ@w:
12*x^3 + 24*x^2 + 10*x + 1
FDUbW:
13*x^3 + 25*x^2 + 10*x + 1
F`IZo:
14*x^3 + 25*x^2 + 10*x + 1
FI_xw:
12*x^3 + 23*x^2 + 10*x + 1
FaG{w:
13*x^3 + 24*x^2 + 10*x + 1
F`H[w:
14*x^3 + 24*x^2 + 10*x + 1
FBZDw:
16*x^3 + 29*x^2 + 11*x + 1
FSOzw:
16*x^3 + 28*x^2 + 11*x + 1
FI_zw:
14*x^3 + 27*x^2 + 11*x + 1
FB`lw:
15*x^3 + 28*x^2 + 11*x + 1
F`H\w:
16*x^3 + 28*x^2 + 11*x + 1
FI_~w:
18*x^3 + 32*x^2 + 12*x + 1
FKcqW:
11*x^3 + 21*x^2 + 9*x + 1
F@Tl_:
8*x^3 + 20*x^2 + 9*x + 1
FAdtO:
9*x^3 + 21*x^2 + 9*x + 1
F@LuO:
8*x^3 + 20*x^2 + 9*x + 1
F`Maw:
14*x^3 + 25*x^2 + 10*x + 1
FDdbW:
12*x^3 + 25*x^2 + 10*x + 1
FJQHw:
11*x^3 + 24*x^2 + 10*x + 1
F@nBg:
12*x^3 + 25*x^2 + 10*x + 1
F`Oxw:
12*x^3 + 23*x^2 + 10*x + 1
FoCyw:
13*x^3 + 24*x^2 + 10*x + 1
FJQLw:
15*x^3 + 29*x^2 + 11*x + 1
F`_zw:
16*x^3 + 28*x^2 + 11*x + 1
FDPlw:
14*x^3 + 28*x^2 + 11*x + 1
FGdrw:
13*x^3 + 27*x^2 + 11*x + 1
F@ptw:
14*x^3 + 28*x^2 + 11*x + 1
FGdvw:
17*x^3 + 32*x^2 + 12*x + 1
F@]eg:
12*x^3 + 25*x^2 + 10*x + 1
F@X\g:
9*x^3 + 23*x^2 + 10*x + 1
F@UuW:
10*x^3 + 24*x^2 + 10*x + 1
FHFKw:
12*x^3 + 24*x^2 + 10*x + 1
FB_zW:
11*x^3 + 23*x^2 + 10*x + 1
FAgzg:
10*x^3 + 23*x^2 + 10*x + 1
FEHkw:
11*x^3 + 24*x^2 + 10*x + 1
F`Dkw:
13*x^3 + 24*x^2 + 10*x + 1
FAK|W:
8*x^3 + 21*x^2 + 10*x + 1
FCLZW:
9*x^3 + 22*x^2 + 10*x + 1
F@S}W:
8*x^3 + 22*x^2 + 10*x + 1
FGL[w:
10*x^3 + 22*x^2 + 10*x + 1
F_YXw:
11*x^3 + 23*x^2 + 10*x + 1
F@huw:
13*x^3 + 28*x^2 + 11*x + 1
FDO~W:
14*x^3 + 28*x^2 + 11*x + 1
FCLjw:
12*x^3 + 26*x^2 + 11*x + 1
FAMjw:
11*x^3 + 26*x^2 + 11*x + 1
F@qZw:
12*x^3 + 27*x^2 + 11*x + 1
F_S|w:
14*x^3 + 27*x^2 + 11*x + 1
FGc~w:
15*x^3 + 31*x^2 + 12*x + 1
F`KuW:
12*x^3 + 25*x^2 + 10*x + 1
F`Gyw:
12*x^3 + 23*x^2 + 10*x + 1
F`FHw:
11*x^3 + 24*x^2 + 10*x + 1
FOLYw:
11*x^3 + 22*x^2 + 10*x + 1
F_oxw:
10*x^3 + 23*x^2 + 10*x + 1
F`G}w:
14*x^3 + 28*x^2 + 11*x + 1
F_Kzw:
14*x^3 + 26*x^2 + 11*x + 1
F_K}w:
13*x^3 + 27*x^2 + 11*x + 1
F_K~w:
16*x^3 + 31*x^2 + 12*x + 1
F@Neo:
12*x^3 + 25*x^2 + 10*x + 1
F@NMg:
10*x^3 + 24*x^2 + 10*x + 1
F@L^G:
8*x^3 + 23*x^2 + 10*x + 1
FB`kw:
12*x^3 + 24*x^2 + 10*x + 1
F@ozg:
10*x^3 + 23*x^2 + 10*x + 1
F@K}W:
6*x^3 + 21*x^2 + 10*x + 1
F@NNg:
12*x^3 + 28*x^2 + 11*x + 1
F@o~g:
14*x^3 + 28*x^2 + 11*x + 1
F@o}w:
12*x^3 + 27*x^2 + 11*x + 1
F@NJw:
10*x^3 + 26*x^2 + 11*x + 1
F@o~w:
14*x^3 + 31*x^2 + 12*x + 1
FK`zo:
18*x^3 + 30*x^2 + 11*x + 1
FK`~o:
20*x^3 + 35*x^2 + 12*x + 1
FK`zw:
20*x^3 + 33*x^2 + 12*x + 1
FK`~w:
22*x^3 + 38*x^2 + 13*x + 1
FI`|o:
16*x^3 + 30*x^2 + 11*x + 1
FC\ng:
18*x^3 + 34*x^2 + 12*x + 1
FI`|w:
18*x^3 + 33*x^2 + 12*x + 1
FCXzw:
16*x^3 + 31*x^2 + 12*x + 1
FGezw:
16*x^3 + 32*x^2 + 12*x + 1
F_L|w:
18*x^3 + 32*x^2 + 12*x + 1
FCX~w:
20*x^3 + 37*x^2 + 13*x + 1
FGd~_:
16*x^3 + 30*x^2 + 11*x + 1
FG]^g:
17*x^3 + 34*x^2 + 12*x + 1
FGd~g:
18*x^3 + 33*x^2 + 12*x + 1
FGdzw:
14*x^3 + 31*x^2 + 12*x + 1
F@p|w:
15*x^3 + 32*x^2 + 12*x + 1
FGd~w:
19*x^3 + 37*x^2 + 13*x + 1
F_N~o:
22*x^3 + 40*x^2 + 13*x + 1
F_N~w:
24*x^3 + 43*x^2 + 14*x + 1
FEOhW:
7*x^3 + 16*x^2 + 8*x + 1
FGW[g:
5*x^3 + 16*x^2 + 8*x + 1
F?K}_:
4*x^3 + 15*x^2 + 8*x + 1
FoCZW:
10*x^3 + 20*x^2 + 9*x + 1
FWCYw:
9*x^3 + 19*x^2 + 9*x + 1
F_opw:
8*x^3 + 20*x^2 + 9*x + 1
FAU`w:
7*x^3 + 19*x^2 + 9*x + 1
F@N@w:
6*x^3 + 18*x^2 + 9*x + 1
FoCZw:
12*x^3 + 23*x^2 + 10*x + 1
FEGmw:
10*x^3 + 23*x^2 + 10*x + 1
F@NBw:
9*x^3 + 22*x^2 + 10*x + 1
F@NFw:
12*x^3 + 26*x^2 + 11*x + 1
F@K}w:
6*x^3 + 24*x^2 + 11*x + 1
F@K~w:
6*x^3 + 27*x^2 + 12*x + 1
F@N^o:
16*x^3 + 33*x^2 + 12*x + 1
F@N]w:
14*x^3 + 31*x^2 + 12*x + 1
F@N^W:
14*x^3 + 32*x^2 + 12*x + 1
F@L}w:
11*x^3 + 30*x^2 + 12*x + 1
F@N^w:
16*x^3 + 36*x^2 + 13*x + 1
F@L~o:
12*x^3 + 31*x^2 + 12*x + 1
F@L|w:
9*x^3 + 28*x^2 + 12*x + 1
F@L~w:
12*x^3 + 34*x^2 + 13*x + 1
F@N~o:
18*x^3 + 38*x^2 + 13*x + 1
F@N~w:
18*x^3 + 41*x^2 + 14*x + 1
FBY^G:
18*x^3 + 30*x^2 + 11*x + 1
FIK}W:
14*x^3 + 28*x^2 + 11*x + 1
FIo|g:
18*x^3 + 30*x^2 + 11*x + 1
F@\sw:
12*x^3 + 27*x^2 + 11*x + 1
FC\rW:
14*x^3 + 28*x^2 + 11*x + 1
FCdzo:
14*x^3 + 28*x^2 + 11*x + 1
FAY|o:
16*x^3 + 29*x^2 + 11*x + 1
FINLw:
20*x^3 + 34*x^2 + 12*x + 1
FBYZw:
16*x^3 + 32*x^2 + 12*x + 1
FAmrw:
18*x^3 + 33*x^2 + 12*x + 1
FC\vW:
20*x^3 + 34*x^2 + 12*x + 1
FBY^w:
22*x^3 + 38*x^2 + 13*x + 1
FBY^?:
16*x^3 + 26*x^2 + 10*x + 1
FLr@w:
20*x^3 + 31*x^2 + 11*x + 1
FF`jW:
18*x^3 + 30*x^2 + 11*x + 1
FAM~O:
15*x^3 + 29*x^2 + 11*x + 1
F_L|o:
16*x^3 + 29*x^2 + 11*x + 1
F@N^O:
14*x^3 + 29*x^2 + 11*x + 1
Fk_zw:
22*x^3 + 35*x^2 + 12*x + 1
FC^bw:
20*x^3 + 34*x^2 + 12*x + 1
FGnRw:
19*x^3 + 34*x^2 + 12*x + 1
F_]vw:
24*x^3 + 39*x^2 + 13*x + 1
F_|tg:
22*x^3 + 36*x^2 + 12*x + 1
FFo~W:
26*x^3 + 41*x^2 + 13*x + 1
FWN]w:
26*x^3 + 40*x^2 + 13*x + 1
FC^vW:
24*x^3 + 40*x^2 + 13*x + 1
FENnw:
28*x^3 + 45*x^2 + 14*x + 1
FBd~W:
22*x^3 + 39*x^2 + 13*x + 1
FC\zw:
18*x^3 + 36*x^2 + 13*x + 1
FAmzw:
19*x^3 + 37*x^2 + 13*x + 1
FC\~W:
22*x^3 + 38*x^2 + 13*x + 1
FC\~w:
24*x^3 + 43*x^2 + 14*x + 1
FBNmw:
21*x^3 + 39*x^2 + 13*x + 1
F@t~g:
22*x^3 + 39*x^2 + 13*x + 1
F@\}w:
16*x^3 + 36*x^2 + 13*x + 1
F@]}w:
18*x^3 + 37*x^2 + 13*x + 1
F@^^w:
23*x^3 + 43*x^2 + 14*x + 1
FG]}w:
20*x^3 + 38*x^2 + 13*x + 1
F_]~w:
26*x^3 + 44*x^2 + 14*x + 1
F@v~w:
30*x^3 + 50*x^2 + 15*x + 1
FBejW:
16*x^3 + 29*x^2 + 11*x + 1
FEXhw:
14*x^3 + 28*x^2 + 11*x + 1
FELlW:
16*x^3 + 29*x^2 + 11*x + 1
FGlug:
17*x^3 + 30*x^2 + 11*x + 1
FBUlW:
15*x^3 + 29*x^2 + 11*x + 1
FIS|W:
13*x^3 + 28*x^2 + 11*x + 1
FBMmW:
15*x^3 + 29*x^2 + 11*x + 1
FJQ\W:
16*x^3 + 30*x^2 + 11*x + 1
FAd|o:
13*x^3 + 28*x^2 + 11*x + 1
FAizo:
14*x^3 + 29*x^2 + 11*x + 1
F@L}o:
11*x^3 + 27*x^2 + 11*x + 1
FG[}g:
12*x^3 + 28*x^2 + 11*x + 1
F@h}o:
14*x^3 + 29*x^2 + 11*x + 1
FEW~W:
20*x^3 + 34*x^2 + 12*x + 1
FHNMw:
19*x^3 + 34*x^2 + 12*x + 1
FClrw:
17*x^3 + 33*x^2 + 12*x + 1
FA]rw:
15*x^3 + 32*x^2 + 12*x + 1
F@nRw:
17*x^3 + 33*x^2 + 12*x + 1
FG^Tw:
18*x^3 + 34*x^2 + 12*x + 1
FA]vw:
21*x^3 + 38*x^2 + 13*x + 1
FG\sw:
12*x^3 + 28*x^2 + 11*x + 1
FIS|w:
15*x^3 + 32*x^2 + 12*x + 1
FA\tw:
14*x^3 + 32*x^2 + 12*x + 1
F@\tw:
14*x^3 + 31*x^2 + 12*x + 1
F@\vw:
16*x^3 + 36*x^2 + 13*x + 1
FHL[w:
13*x^3 + 27*x^2 + 11*x + 1
F@T|o:
11*x^3 + 27*x^2 + 11*x + 1
F@]uW:
13*x^3 + 29*x^2 + 11*x + 1
F@L|o:
9*x^3 + 25*x^2 + 11*x + 1
FHM]w:
18*x^3 + 33*x^2 + 12*x + 1
F@]uw:
16*x^3 + 33*x^2 + 12*x + 1
F@]rw:
14*x^3 + 31*x^2 + 12*x + 1
F@]vw:
19*x^3 + 37*x^2 + 13*x + 1
F@^vo:
24*x^3 + 40*x^2 + 13*x + 1
FHN]w:
23*x^3 + 39*x^2 + 13*x + 1
F@l~g:
20*x^3 + 38*x^2 + 13*x + 1
F@^vw:
25*x^3 + 44*x^2 + 14*x + 1
F@\~g:
17*x^3 + 37*x^2 + 13*x + 1
F@\|w:
15*x^3 + 35*x^2 + 13*x + 1
F@\~w:
18*x^3 + 41*x^2 + 14*x + 1
F@]~w:
21*x^3 + 42*x^2 + 14*x + 1
F@^~w:
27*x^3 + 49*x^2 + 15*x + 1
F@~vg:
32*x^3 + 47*x^2 + 14*x + 1
F@~uw:
28*x^3 + 46*x^2 + 14*x + 1
F@^~o:
26*x^3 + 45*x^2 + 14*x + 1
F@~vw:
34*x^3 + 52*x^2 + 15*x + 1
F@~~w:
36*x^3 + 57*x^2 + 16*x + 1
FBY~o:
24*x^3 + 40*x^2 + 13*x + 1
FDhzw:
22*x^3 + 38*x^2 + 13*x + 1
FBY}w:
22*x^3 + 39*x^2 + 13*x + 1
FBX|w:
18*x^3 + 37*x^2 + 13*x + 1
FHU}w:
23*x^3 + 39*x^2 + 13*x + 1
FBY~w:
26*x^3 + 44*x^2 + 14*x + 1
FI\tw:
18*x^3 + 38*x^2 + 13*x + 1
FBX~w:
20*x^3 + 42*x^2 + 14*x + 1
FBZ~o:
28*x^3 + 46*x^2 + 14*x + 1
FBZ~w:
30*x^3 + 50*x^2 + 15*x + 1
F?]u_:
11*x^3 + 21*x^2 + 9*x + 1
FWD[o:
11*x^3 + 21*x^2 + 9*x + 1
FGc}_:
11*x^3 + 21*x^2 + 9*x + 1
FBj@w:
14*x^3 + 25*x^2 + 10*x + 1
F`YPw:
14*x^3 + 25*x^2 + 10*x + 1
FIe`w:
14*x^3 + 25*x^2 + 10*x + 1
FIebw:
17*x^3 + 29*x^2 + 11*x + 1
FIefw:
20*x^3 + 33*x^2 + 12*x + 1
comment: This is the wheel $W_7$.
FHo}g:
18*x^3 + 30*x^2 + 11*x + 1
FM`hw:
18*x^3 + 30*x^2 + 11*x + 1
Fie`w:
19*x^3 + 31*x^2 + 11*x + 1
FKK}W:
17*x^3 + 29*x^2 + 11*x + 1
F`Lkw:
17*x^3 + 29*x^2 + 11*x + 1
FKL\W:
17*x^3 + 29*x^2 + 11*x + 1
FY_}w:
22*x^3 + 35*x^2 + 12*x + 1
FKNJw:
21*x^3 + 34*x^2 + 12*x + 1
FKNNw:
25*x^3 + 39*x^2 + 13*x + 1
FHU^G:
16*x^3 + 30*x^2 + 11*x + 1
FKWyw:
14*x^3 + 28*x^2 + 11*x + 1
FIMmw:
19*x^3 + 34*x^2 + 12*x + 1
FHd\w:
19*x^3 + 33*x^2 + 12*x + 1
FKL^W:
20*x^3 + 34*x^2 + 12*x + 1
FHUZw:
16*x^3 + 32*x^2 + 12*x + 1
FHU^w:
22*x^3 + 38*x^2 + 13*x + 1
FJQ\O:
15*x^3 + 26*x^2 + 10*x + 1
FHU^?:
14*x^3 + 26*x^2 + 10*x + 1
Fbj@w:
18*x^3 + 31*x^2 + 11*x + 1
FDprW:
17*x^3 + 30*x^2 + 11*x + 1
FIdtW:
16*x^3 + 30*x^2 + 11*x + 1
FIc~G:
17*x^3 + 30*x^2 + 11*x + 1
FIM\W:
16*x^3 + 29*x^2 + 11*x + 1
Fh_}w:
21*x^3 + 35*x^2 + 12*x + 1
FSTjw:
21*x^3 + 34*x^2 + 12*x + 1
FDZJw:
20*x^3 + 34*x^2 + 12*x + 1
FIejw:
19*x^3 + 34*x^2 + 12*x + 1
FoL^w:
24*x^3 + 39*x^2 + 13*x + 1
Fbc~W:
26*x^3 + 41*x^2 + 13*x + 1
FQdzw:
25*x^3 + 39*x^2 + 13*x + 1
FKNmw:
25*x^3 + 40*x^2 + 13*x + 1
FQL}w:
24*x^3 + 39*x^2 + 13*x + 1
FHd}w:
23*x^3 + 39*x^2 + 13*x + 1
FoNZw:
25*x^3 + 40*x^2 + 13*x + 1
FaM~w:
29*x^3 + 45*x^2 + 14*x + 1
FB]vW:
23*x^3 + 40*x^2 + 13*x + 1
FBhzw:
19*x^3 + 37*x^2 + 13*x + 1
FBh|w:
21*x^3 + 38*x^2 + 13*x + 1
FBh~w:
26*x^3 + 44*x^2 + 14*x + 1
FB]uW:
19*x^3 + 35*x^2 + 12*x + 1
FBY}o:
20*x^3 + 35*x^2 + 12*x + 1
FDp~o:
25*x^3 + 41*x^2 + 13*x + 1
FBh}w:
22*x^3 + 39*x^2 + 13*x + 1
FDpzw:
23*x^3 + 39*x^2 + 13*x + 1
FBj^w:
28*x^3 + 45*x^2 + 14*x + 1
FBj~o:
30*x^3 + 47*x^2 + 14*x + 1
FBj~w:
33*x^3 + 51*x^2 + 15*x + 1
Fo\sw:
24*x^3 + 36*x^2 + 12*x + 1
FIU|o:
22*x^3 + 35*x^2 + 12*x + 1
FBY|o:
20*x^3 + 34*x^2 + 12*x + 1
FbY\w:
28*x^3 + 41*x^2 + 13*x + 1
FImrw:
26*x^3 + 40*x^2 + 13*x + 1
FImvw:
32*x^3 + 46*x^2 + 14*x + 1
FQ\sw:
22*x^3 + 35*x^2 + 12*x + 1
FJY[w:
20*x^3 + 35*x^2 + 12*x + 1
FB\tW:
16*x^3 + 33*x^2 + 12*x + 1
F`Lzo:
18*x^3 + 33*x^2 + 12*x + 1
FXT[w:
22*x^3 + 35*x^2 + 12*x + 1
F@\~_:
16*x^3 + 33*x^2 + 12*x + 1
FB]^G:
20*x^3 + 35*x^2 + 12*x + 1
FJY\w:
24*x^3 + 40*x^2 + 13*x + 1
F`\tw:
26*x^3 + 40*x^2 + 13*x + 1
FJYZw:
20*x^3 + 38*x^2 + 13*x + 1
FB^dw:
24*x^3 + 40*x^2 + 13*x + 1
FJY^w:
28*x^3 + 45*x^2 + 14*x + 1
FT\uW:
28*x^3 + 42*x^2 + 13*x + 1
FI}vg:
34*x^3 + 48*x^2 + 14*x + 1
Fdhzw:
34*x^3 + 47*x^2 + 14*x + 1
FInvw:
38*x^3 + 53*x^2 + 15*x + 1
FLh}w:
32*x^3 + 47*x^2 + 14*x + 1
FS\zw:
30*x^3 + 45*x^2 + 14*x + 1
FIm~w:
36*x^3 + 52*x^2 + 15*x + 1
FIn~w:
42*x^3 + 59*x^2 + 16*x + 1
FIl~g:
30*x^3 + 46*x^2 + 14*x + 1
FI]|w:
28*x^3 + 45*x^2 + 14*x + 1
FJY}w:
28*x^3 + 46*x^2 + 14*x + 1
FI]~w:
32*x^3 + 51*x^2 + 15*x + 1
FI\|w:
22*x^3 + 43*x^2 + 14*x + 1
FB\|w:
21*x^3 + 42*x^2 + 14*x + 1
FB\~w:
24*x^3 + 48*x^2 + 15*x + 1
FD\~W:
28*x^3 + 45*x^2 + 14*x + 1
FB]~W:
27*x^3 + 45*x^2 + 14*x + 1
FB]|w:
24*x^3 + 43*x^2 + 14*x + 1
FB]~w:
30*x^3 + 50*x^2 + 15*x + 1
FB^~w:
36*x^3 + 57*x^2 + 16*x + 1
FkUhw:
24*x^3 + 36*x^2 + 12*x + 1
FsLZW:
23*x^3 + 36*x^2 + 12*x + 1
FHU}o:
21*x^3 + 35*x^2 + 12*x + 1
Fo^Pw:
22*x^3 + 36*x^2 + 12*x + 1
F@]~_:
19*x^3 + 34*x^2 + 12*x + 1
FA]~_:
20*x^3 + 35*x^2 + 12*x + 1
FpUZw:
28*x^3 + 41*x^2 + 13*x + 1
Fbh\w:
27*x^3 + 41*x^2 + 13*x + 1
FBnbw:
25*x^3 + 40*x^2 + 13*x + 1
FFYmw:
26*x^3 + 41*x^2 + 13*x + 1
FBnfw:
31*x^3 + 46*x^2 + 14*x + 1
FDx~g:
32*x^3 + 47*x^2 + 14*x + 1
FPvZw:
31*x^3 + 46*x^2 + 14*x + 1
FBnvW:
31*x^3 + 47*x^2 + 14*x + 1
FHu~w:
35*x^3 + 52*x^2 + 15*x + 1
FBy}w:
29*x^3 + 46*x^2 + 14*x + 1
FB]}w:
25*x^3 + 44*x^2 + 14*x + 1
FBn^w:
32*x^3 + 51*x^2 + 15*x + 1
FBn~w:
39*x^3 + 58*x^2 + 16*x + 1
FF^nW:
40*x^3 + 54*x^2 + 15*x + 1
FI~tw:
38*x^3 + 54*x^2 + 15*x + 1
FB^~o:
34*x^3 + 52*x^2 + 15*x + 1
FBn~o:
36*x^3 + 53*x^2 + 15*x + 1
FB~vw:
44*x^3 + 60*x^2 + 16*x + 1
FB~~w:
48*x^3 + 66*x^2 + 17*x + 1
F@~v_:
30*x^3 + 42*x^2 + 13*x + 1
FbY|o:
30*x^3 + 42*x^2 + 13*x + 1
FFzbw:
36*x^3 + 48*x^2 + 14*x + 1
FFzfw:
42*x^3 + 54*x^2 + 15*x + 1
FK~v_:
36*x^3 + 49*x^2 + 14*x + 1
F]p|w:
42*x^3 + 55*x^2 + 15*x + 1
Fs\zw:
42*x^3 + 54*x^2 + 15*x + 1
Fs\~w:
48*x^3 + 61*x^2 + 16*x + 1
FFz~o:
48*x^3 + 62*x^2 + 16*x + 1
FFz~w:
54*x^3 + 68*x^2 + 17*x + 1
FF~~w:
60*x^3 + 75*x^2 + 18*x + 1
FGeZ_:
9*x^3 + 21*x^2 + 9*x + 1
FJaHw:
12*x^3 + 25*x^2 + 10*x + 1
F`N@w:
12*x^3 + 25*x^2 + 10*x + 1
FJaJw:
15*x^3 + 29*x^2 + 11*x + 1
FJaNw:
18*x^3 + 33*x^2 + 12*x + 1
FaK|W:
17*x^3 + 29*x^2 + 11*x + 1
FPLYw:
13*x^3 + 27*x^2 + 11*x + 1
FKcyw:
16*x^3 + 28*x^2 + 11*x + 1
FEXlw:
19*x^3 + 34*x^2 + 12*x + 1
FHeZw:
18*x^3 + 33*x^2 + 12*x + 1
FPTZw:
17*x^3 + 32*x^2 + 12*x + 1
FKW}w:
19*x^3 + 34*x^2 + 12*x + 1
F`MZw:
20*x^3 + 33*x^2 + 12*x + 1
FPT^w:
22*x^3 + 38*x^2 + 13*x + 1
FJYKg:
13*x^3 + 26*x^2 + 10*x + 1
FJ_}W:
16*x^3 + 30*x^2 + 11*x + 1
FKdjg:
16*x^3 + 30*x^2 + 11*x + 1
FjaHw:
17*x^3 + 31*x^2 + 11*x + 1
comment: This is the Moser spindle.
FKLkw:
15*x^3 + 29*x^2 + 11*x + 1
F`K}W:
15*x^3 + 29*x^2 + 11*x + 1
FwC}w:
20*x^3 + 35*x^2 + 12*x + 1
FKYZw:
19*x^3 + 34*x^2 + 12*x + 1
F`NNw:
23*x^3 + 39*x^2 + 13*x + 1
F`Kyw:
15*x^3 + 27*x^2 + 11*x + 1
F`K}w:
18*x^3 + 33*x^2 + 12*x + 1
F`Kzw:
18*x^3 + 31*x^2 + 12*x + 1
F`K~w:
21*x^3 + 37*x^2 + 13*x + 1
FeK~W:
25*x^3 + 41*x^2 + 13*x + 1
FKdzw:
23*x^3 + 39*x^2 + 13*x + 1
FQT|w:
23*x^3 + 39*x^2 + 13*x + 1
F`N^W:
24*x^3 + 40*x^2 + 13*x + 1
F`N^w:
28*x^3 + 45*x^2 + 14*x + 1
F`L~o:
24*x^3 + 40*x^2 + 13*x + 1
F`Lzw:
21*x^3 + 37*x^2 + 13*x + 1
F`L|w:
24*x^3 + 38*x^2 + 13*x + 1
F`L~w:
27*x^3 + 44*x^2 + 14*x + 1
F`N~o:
30*x^3 + 47*x^2 + 14*x + 1
F`N~w:
33*x^3 + 51*x^2 + 15*x + 1
FKzPw:
22*x^3 + 36*x^2 + 12*x + 1
FQT|o:
20*x^3 + 35*x^2 + 12*x + 1
FI]\g:
20*x^3 + 35*x^2 + 12*x + 1
FwL[w:
22*x^3 + 36*x^2 + 12*x + 1
FB]lg:
18*x^3 + 34*x^2 + 12*x + 1
Fbo|w:
26*x^3 + 41*x^2 + 13*x + 1
FJejw:
24*x^3 + 40*x^2 + 13*x + 1
FJenw:
30*x^3 + 46*x^2 + 14*x + 1
Fkoxw:
23*x^3 + 36*x^2 + 12*x + 1
FpLYw:
22*x^3 + 35*x^2 + 12*x + 1
FkYXw:
22*x^3 + 36*x^2 + 12*x + 1
FPT}o:
21*x^3 + 35*x^2 + 12*x + 1
F`L|o:
21*x^3 + 34*x^2 + 12*x + 1
F`v`w:
21*x^3 + 36*x^2 + 12*x + 1
FpL]w:
27*x^3 + 41*x^2 + 13*x + 1
F`]rw:
26*x^3 + 40*x^2 + 13*x + 1
Fbg}w:
26*x^3 + 41*x^2 + 13*x + 1
F`]vw:
31*x^3 + 46*x^2 + 14*x + 1
FJ]^G:
25*x^3 + 41*x^2 + 13*x + 1
FL]uW:
27*x^3 + 42*x^2 + 13*x + 1
FJnNg:
33*x^3 + 48*x^2 + 14*x + 1
FTpzw:
32*x^3 + 47*x^2 + 14*x + 1
FJq~w:
37*x^3 + 53*x^2 + 15*x + 1
FJd~W:
29*x^3 + 46*x^2 + 14*x + 1
FK\zw:
24*x^3 + 43*x^2 + 14*x + 1
FK\|w:
28*x^3 + 45*x^2 + 14*x + 1
F`\|w:
30*x^3 + 45*x^2 + 14*x + 1
FK\~w:
33*x^3 + 51*x^2 + 15*x + 1
FTX}w:
31*x^3 + 47*x^2 + 14*x + 1
FK]~w:
35*x^3 + 52*x^2 + 15*x + 1
F`l~g:
32*x^3 + 47*x^2 + 14*x + 1
F`t|w:
30*x^3 + 46*x^2 + 14*x + 1
F`]~w:
36*x^3 + 52*x^2 + 15*x + 1
FK^~w:
42*x^3 + 59*x^2 + 16*x + 1
Ftpzw:
41*x^3 + 55*x^2 + 15*x + 1
FK^~o:
38*x^3 + 54*x^2 + 15*x + 1
FK~vw:
46*x^3 + 61*x^2 + 16*x + 1
FK~~w:
51*x^3 + 67*x^2 + 17*x + 1
FJY}o:
26*x^3 + 41*x^2 + 13*x + 1
FJvdw:
33*x^3 + 48*x^2 + 14*x + 1
FLpzw:
31*x^3 + 46*x^2 + 14*x + 1
FLp|w:
32*x^3 + 47*x^2 + 14*x + 1
Fbh|w:
33*x^3 + 47*x^2 + 14*x + 1
FLp~w:
38*x^3 + 53*x^2 + 15*x + 1
FLr~o:
40*x^3 + 55*x^2 + 15*x + 1
FLr~w:
45*x^3 + 60*x^2 + 16*x + 1
FBnvO:
28*x^3 + 42*x^2 + 13*x + 1
F`]~_:
28*x^3 + 42*x^2 + 13*x + 1
Fb]lg:
28*x^3 + 42*x^2 + 13*x + 1
FLvbw:
34*x^3 + 48*x^2 + 14*x + 1
FLvfw:
40*x^3 + 54*x^2 + 15*x + 1
FLvvO:
35*x^3 + 49*x^2 + 14*x + 1
Flp|w:
41*x^3 + 55*x^2 + 15*x + 1
FM^lw:
39*x^3 + 54*x^2 + 15*x + 1
Fk]~w:
47*x^3 + 61*x^2 + 16*x + 1
FJn^W:
38*x^3 + 54*x^2 + 15*x + 1
FJ]}w:
34*x^3 + 52*x^2 + 15*x + 1
FJn^w:
44*x^3 + 60*x^2 + 16*x + 1
Fbn~w:
54*x^3 + 68*x^2 + 17*x + 1
FZn]w:
49*x^3 + 62*x^2 + 16*x + 1
FLv~o:
48*x^3 + 62*x^2 + 16*x + 1
FL~vw:
56*x^3 + 69*x^2 + 17*x + 1
FL~~w:
63*x^3 + 76*x^2 + 18*x + 1
FU\~W:
40*x^3 + 54*x^2 + 15*x + 1
Fb]|w:
39*x^3 + 53*x^2 + 15*x + 1
FLl}w:
37*x^3 + 53*x^2 + 15*x + 1
FR^^w:
45*x^3 + 60*x^2 + 16*x + 1
FJm~w:
42*x^3 + 59*x^2 + 16*x + 1
FJn~w:
51*x^3 + 67*x^2 + 17*x + 1
FR\}w:
36*x^3 + 52*x^2 + 15*x + 1
FJ]|w:
33*x^3 + 51*x^2 + 15*x + 1
FJ]~w:
39*x^3 + 58*x^2 + 16*x + 1
FJ\|w:
27*x^3 + 49*x^2 + 15*x + 1
FJ\~w:
30*x^3 + 55*x^2 + 16*x + 1
FJ^~w:
45*x^3 + 65*x^2 + 17*x + 1
FJ~~w:
60*x^3 + 75*x^2 + 18*x + 1
FN~~w:
75*x^3 + 85*x^2 + 19*x + 1
FJn~o:
46*x^3 + 61*x^2 + 16*x + 1
FJ^~o:
42*x^3 + 59*x^2 + 16*x + 1
Fj]|w:
48*x^3 + 61*x^2 + 16*x + 1
FJ~vw:
54*x^3 + 68*x^2 + 17*x + 1
Fjm~w:
57*x^3 + 69*x^2 + 17*x + 1
FNz~w:
66*x^3 + 77*x^2 + 18*x + 1
FNz~o:
58*x^3 + 70*x^2 + 17*x + 1
F]~vw:
68*x^3 + 78*x^2 + 18*x + 1
F]~~w:
78*x^3 + 86*x^2 + 19*x + 1
F^~~w:
90*x^3 + 95*x^2 + 20*x + 1
F~~~w:
105*x^3 + 105*x^2 + 21*x + 1
comment: This is the complete graph $K_7$.
Definition
For a connected simple graph $G$, let $m_k(G)$ be the number of matchings with $k$ edges and let $m_0(G)=1$. Listed is the matching-generating polynomial $M(G,x)=\sum_{k\geq0}m_k(G)x^k$ [1] [2].
Parameters
$G$
—   graph (a connected simple graph, named by its canonical graph6 string)
Formulas
(1)
If $G$ has $n$ vertices and $\mu(G,x)$ is the signed matching polynomial, then $\mu(G,x)=x^nM(G,-x^{-2})$.
(2)
$M(G,x)=I(L(G),x)$, where $I$ is the independence polynomial and $L(G)$ is the line graph of $G$.
Comments
(3)
Graphs are named by their graph6 string [3], 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 used here with g.canonical_label(algorithm='sage').graph6_string(). The same names index the chromatic polynomials and the Tutte polynomials.
(4)
$M(G,x)$ records the matching counts $m_k(G)$ directly. It does not record the number of vertices, so graphs of different sizes can share it: $K_3$ and $K_{1,3}$ have $M(G,x)=3x+1$.
(5)
$M(G,1)=\sum_k m_k(G)$ is the number of matchings of $G$, called its Hosoya index; for $K_7$ it is $232$.
(6)
The 996 graphs here have 379 distinct matching-generating polynomials. The largest class of connected graphs with the same matching-generating polynomial has 13 graphs.
Programs
(P1)
Sage
from sage.graphs.graph import Graph

G = Graph('EIe_')                  # C_6, by its name here
mu = G.matching_polynomial()
x = mu.parent().gen()
n = G.num_verts()
sum(abs(mu[n - 2*k]) * x**k for k in range(n // 2 + 1))
Links
Similar tables
Signed matching polynomials of connected graphs —   uses the same graph names and stores $\mu(G,x)=\sum_k(-1)^k m_k(G)x^{n-2k}$; for a graph with $n$ vertices, $\mu(G,x)=x^nM(G,-x^{-2})$, so the two tables encode the same matching counts in different one-variable polynomials. This table is the likely target for a reader holding matching counts or a Hosoya-index computation; the signed table is the convention used for roots and characteristic-polynomial identities.
Independence polynomials of trees —   for every graph $G$, $M(G,x)$ is the independence polynomial $I(L(G),x)$ of its line graph
Chromatic polynomials of connected graphs —   uses the same canonical graph6 index for connected graphs on at most seven vertices
Tutte polynomials of connected graphs —   uses the same canonical graph6 index for connected graphs on at most seven vertices, but the matching-generating polynomial is not determined by the Tutte polynomial
Entropy constants of lattice models —   the dimer model counts perfect matchings of lattice regions; for a graph $G$ with an even number $n$ of vertices, the coefficient of $x^{n/2}$ in $M(G,x)$ counts perfect matchings
Data properties
Entries are of type: integral polynomial
How well the digits are known: exact
Table is complete: no (it holds $M(G,x)$ for every connected graph $G$ on at most seven vertices)
How they were obtained:

The generator enumerates connected simple graphs with $1\leq |V(G)|\leq7$ using Sage, takes each graph's canonical_label(algorithm='sage'), and stores the canonical graph6 string. It counts matchings by exact enumeration of edge subsets and forms $M(G,x)$ over $\mathbb{Z}[x]$.

more

The 996 graph6 strings are exactly the keys of the chromatic polynomial table and the Tutte polynomial table. The count of equal-polynomial classes in comment (6) was computed from the same exact rows. Formula (1) agreed against the stored signed rows before the split, and formula (2) agreed on the 109 graphs whose line graph is connected and has at most seven vertices.



API Python package Skill for AI Privacy Legal notice Source
Data licensed CC BY-SA 4.0. No tracking, no analytics, essential cookies only.