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{
"T237": {
"title": "Characteristic polynomials of connected graphs",
"numbers": {
"A_": {
"number": "x^2 - 1",
"comment": "This is the complete graph $K_2$."
},
"BW": {
"number": "x^3 - 2*x",
"comment": "This is the path $P_3$."
},
"Bw": {
"number": "x^3 - 3*x - 2",
"comment": "This is the complete graph $K_3$."
},
"CF": {
"number": "x^4 - 3*x^2",
"comment": "This is the star $K_{1,3}$."
},
"CL": {
"number": "x^4 - 3*x^2 + 1",
"comment": "This is the path $P_4$."
},
"CN": "x^4 - 4*x^2 - 2*x + 1",
"C]": {
"number": "x^4 - 4*x^2",
"comment": "This is the cycle $C_4$."
},
"C^": {
"number": "x^4 - 5*x^2 - 4*x",
"comment": "This is the diamond graph."
},
"C~": {
"number": "x^4 - 6*x^2 - 8*x - 3",
"comment": "This is the complete graph $K_4$."
},
"D?{": {
"number": "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": {
"number": "x^5 - 5*x^3 - 2*x^2 + 3*x",
"comment": "This is the bull graph."
},
"DB{": {
"number": "x^5 - 6*x^3 - 4*x^2 + 2*x",
"comment": "This is the dart graph."
},
"DFw": {
"number": "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": {
"number": "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{": {
"number": "x^5 - 6*x^3 - 4*x^2 + 5*x + 4",
"comment": "This is the butterfly graph."
},
"DLo": {
"number": "x^5 - 5*x^3 + 5*x - 2",
"comment": "This is the cycle $C_5$."
},
"Dbk": {
"number": "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{": {
"number": "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]{": {
"number": "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~{": {
"number": "x^5 - 10*x^3 - 20*x^2 - 15*x - 4",
"comment": "This is the complete graph $K_5$."
},
"E?Bw": {
"number": "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": {
"number": "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": {
"number": "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": {
"number": "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_": {
"number": "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": {
"number": "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_": {
"number": "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": {
"number": "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": {
"number": "x^6 - 15*x^4 - 40*x^3 - 45*x^2 - 24*x - 5",
"comment": "This is the complete graph $K_6$."
}
}
},
"T238": {
"title": "Laplacian polynomials of connected graphs",
"numbers": {
"A_": {
"number": "x^2 - 2*x",
"comment": "This is the complete graph $K_2$."
},
"BW": {
"number": "x^3 - 4*x^2 + 3*x",
"comment": "This is the path $P_3$."
},
"Bw": {
"number": "x^3 - 6*x^2 + 9*x",
"comment": "This is the complete graph $K_3$."
},
"CF": {
"number": "x^4 - 6*x^3 + 9*x^2 - 4*x",
"comment": "This is the star $K_{1,3}$."
},
"CL": {
"number": "x^4 - 6*x^3 + 10*x^2 - 4*x",
"comment": "This is the path $P_4$."
},
"CN": "x^4 - 8*x^3 + 19*x^2 - 12*x",
"C]": {
"number": "x^4 - 8*x^3 + 20*x^2 - 16*x",
"comment": "This is the cycle $C_4$."
},
"C^": {
"number": "x^4 - 10*x^3 + 32*x^2 - 32*x",
"comment": "This is the diamond graph."
},
"C~": {
"number": "x^4 - 12*x^3 + 48*x^2 - 64*x",
"comment": "This is the complete graph $K_4$."
},
"D?{": {
"number": "x^5 - 8*x^4 + 18*x^3 - 16*x^2 + 5*x",
"comment": "This is the star $K_{1,4}$."
},
"D@s": "x^5 - 8*x^4 + 20*x^3 - 18*x^2 + 5*x",
"D@{": "x^5 - 10*x^4 + 32*x^3 - 38*x^2 + 15*x",
"DIk": "x^5 - 10*x^4 + 34*x^3 - 46*x^2 + 20*x",
"DBk": {
"number": "x^5 - 10*x^4 + 33*x^3 - 40*x^2 + 15*x",
"comment": "This is the bull graph."
},
"DB{": {
"number": "x^5 - 12*x^4 + 49*x^3 - 78*x^2 + 40*x",
"comment": "This is the dart graph."
},
"DFw": {
"number": "x^5 - 12*x^4 + 51*x^3 - 92*x^2 + 60*x",
"comment": "This is the complete bipartite graph $K_{2,3}$."
},
"DF{": "x^5 - 14*x^4 + 69*x^3 - 140*x^2 + 100*x",
"DBg": {
"number": "x^5 - 8*x^4 + 21*x^3 - 20*x^2 + 5*x",
"comment": "This is the path $P_5$."
},
"DK[": "x^5 - 10*x^4 + 34*x^3 - 44*x^2 + 15*x",
"DK{": {
"number": "x^5 - 12*x^4 + 50*x^3 - 84*x^2 + 45*x",
"comment": "This is the butterfly graph."
},
"DLo": {
"number": "x^5 - 10*x^4 + 35*x^3 - 50*x^2 + 25*x",
"comment": "This is the cycle $C_5$."
},
"Dbk": {
"number": "x^5 - 12*x^4 + 51*x^3 - 90*x^2 + 55*x",
"comment": "This is the house graph."
},
"DL{": "x^5 - 14*x^4 + 70*x^3 - 146*x^2 + 105*x",
"DJk": "x^5 - 12*x^4 + 50*x^3 - 82*x^2 + 40*x",
"DJ{": "x^5 - 14*x^4 + 69*x^3 - 136*x^2 + 80*x",
"DN{": {
"number": "x^5 - 16*x^4 + 93*x^3 - 230*x^2 + 200*x",
"comment": "This is the house X graph."
},
"DNw": "x^5 - 14*x^4 + 71*x^3 - 154*x^2 + 120*x",
"D]{": {
"number": "x^5 - 16*x^4 + 94*x^3 - 240*x^2 + 225*x",
"comment": "This is the wheel $W_5$."
},
"D^{": "x^5 - 18*x^4 + 120*x^3 - 350*x^2 + 375*x",
"D~{": {
"number": "x^5 - 20*x^4 + 150*x^3 - 500*x^2 + 625*x",
"comment": "This is the complete graph $K_5$."
},
"E?Bw": {
"number": "x^6 - 10*x^5 + 30*x^4 - 40*x^3 + 25*x^2 - 6*x",
"comment": "This is the star $K_{1,5}$."
},
"E?Fg": "x^6 - 10*x^5 + 33*x^4 - 46*x^3 + 28*x^2 - 6*x",
"E?Fw": "x^6 - 12*x^5 + 48*x^4 - 82*x^3 + 63*x^2 - 18*x",
"E@FG": "x^6 - 10*x^5 + 35*x^4 - 52*x^3 + 32*x^2 - 6*x",
"E?NG": "x^6 - 10*x^5 + 34*x^4 - 48*x^3 + 29*x^2 - 6*x",
"E@JW": "x^6 - 12*x^5 + 51*x^4 - 96*x^3 + 80*x^2 - 24*x",
"E?NW": "x^6 - 12*x^5 + 50*x^4 - 88*x^3 + 67*x^2 - 18*x",
"E?Nw": "x^6 - 14*x^5 + 69*x^4 - 148*x^3 + 140*x^2 - 48*x",
"E?]o": "x^6 - 12*x^5 + 52*x^4 - 100*x^3 + 84*x^2 - 24*x",
"E?^o": "x^6 - 14*x^5 + 72*x^4 - 170*x^3 + 184*x^2 - 72*x",
"E?]w": "x^6 - 14*x^5 + 70*x^4 - 152*x^3 + 144*x^2 - 48*x",
"E?^w": "x^6 - 16*x^5 + 93*x^4 - 242*x^3 + 284*x^2 - 120*x",
"E?~o": {
"number": "x^6 - 16*x^5 + 96*x^4 - 272*x^3 + 368*x^2 - 192*x",
"comment": "This is the complete bipartite graph $K_{2,4}$."
},
"E?~w": "x^6 - 18*x^5 + 120*x^4 - 368*x^3 + 528*x^2 - 288*x",
"E@QW": "x^6 - 10*x^5 + 35*x^4 - 52*x^3 + 31*x^2 - 6*x",
"E@`w": "x^6 - 12*x^5 + 51*x^4 - 94*x^3 + 72*x^2 - 18*x",
"E@Rw": "x^6 - 14*x^5 + 70*x^4 - 156*x^3 + 153*x^2 - 54*x",
"E@YW": "x^6 - 12*x^5 + 52*x^4 - 100*x^3 + 83*x^2 - 24*x",
"EHQW": "x^6 - 12*x^5 + 53*x^4 - 106*x^3 + 95*x^2 - 30*x",
"E@UW": "x^6 - 12*x^5 + 51*x^4 - 92*x^3 + 69*x^2 - 18*x",
"EGNW": "x^6 - 14*x^5 + 72*x^4 - 168*x^3 + 176*x^2 - 66*x",
"EAMw": "x^6 - 14*x^5 + 71*x^4 - 158*x^3 + 149*x^2 - 48*x",
"E@Vw": "x^6 - 16*x^5 + 94*x^4 - 250*x^3 + 297*x^2 - 126*x",
"E@YO": {
"number": "x^6 - 10*x^5 + 36*x^4 - 56*x^3 + 35*x^2 - 6*x",
"comment": "This is the path $P_6$."
},
"EI_w": "x^6 - 12*x^5 + 53*x^4 - 106*x^3 + 92*x^2 - 24*x",
"EGdo": "x^6 - 12*x^5 + 53*x^4 - 104*x^3 + 84*x^2 - 18*x",
"EGcw": "x^6 - 12*x^5 + 52*x^4 - 98*x^3 + 76*x^2 - 18*x",
"E@ow": "x^6 - 12*x^5 + 52*x^4 - 98*x^3 + 75*x^2 - 18*x",
"EK`w": {
"number": "x^6 - 14*x^5 + 73*x^4 - 176*x^3 + 192*x^2 - 72*x",
"comment": "It has the same Laplacian polynomial as EBYW."
},
"ECXw": "x^6 - 14*x^5 + 72*x^4 - 166*x^3 + 164*x^2 - 48*x",
"EGdw": "x^6 - 14*x^5 + 72*x^4 - 166*x^3 + 165*x^2 - 54*x",
"E_Nw": "x^6 - 16*x^5 + 95*x^4 - 260*x^3 + 324*x^2 - 144*x",
"E@NW": "x^6 - 14*x^5 + 71*x^4 - 158*x^3 + 148*x^2 - 48*x",
"E@Nw": "x^6 - 16*x^5 + 93*x^4 - 238*x^3 + 256*x^2 - 96*x",
"E_]o": "x^6 - 14*x^5 + 74*x^4 - 184*x^3 + 216*x^2 - 96*x",
"EENg": "x^6 - 16*x^5 + 97*x^4 - 278*x^3 + 376*x^2 - 192*x",
"EC\\w": "x^6 - 16*x^5 + 95*x^4 - 256*x^3 + 304*x^2 - 120*x",
"E@^W": "x^6 - 16*x^5 + 95*x^4 - 256*x^3 + 305*x^2 - 126*x",
"E_]w": "x^6 - 16*x^5 + 96*x^4 - 268*x^3 + 348*x^2 - 168*x",
"E@vw": "x^6 - 18*x^5 + 122*x^4 - 386*x^3 + 568*x^2 - 312*x",
"E@^o": "x^6 - 16*x^5 + 96*x^4 - 266*x^3 + 332*x^2 - 144*x",
"E@]w": "x^6 - 16*x^5 + 94*x^4 - 244*x^3 + 264*x^2 - 96*x",
"E@^w": "x^6 - 18*x^5 + 121*x^4 - 372*x^3 + 508*x^2 - 240*x",
"E@~o": "x^6 - 18*x^5 + 124*x^4 - 408*x^3 + 640*x^2 - 384*x",
"E@~w": "x^6 - 20*x^5 + 152*x^4 - 544*x^3 + 912*x^2 - 576*x",
"EBYW": {
"number": "x^6 - 14*x^5 + 73*x^4 - 176*x^3 + 192*x^2 - 72*x",
"comment": "It has the same Laplacian polynomial as EK`w."
},
"EBYw": "x^6 - 16*x^5 + 96*x^4 - 266*x^3 + 333*x^2 - 144*x",
"EBZw": "x^6 - 18*x^5 + 122*x^4 - 384*x^3 + 549*x^2 - 270*x",
"EIe_": {
"number": "x^6 - 12*x^5 + 54*x^4 - 112*x^3 + 105*x^2 - 36*x",
"comment": "This is the cycle $C_6$."
},
"EKNG": "x^6 - 14*x^5 + 74*x^4 - 184*x^3 + 213*x^2 - 90*x",
"EHUW": "x^6 - 14*x^5 + 73*x^4 - 174*x^3 + 185*x^2 - 66*x",
"EoLW": "x^6 - 14*x^5 + 74*x^4 - 182*x^3 + 205*x^2 - 84*x",
"E@]o": "x^6 - 14*x^5 + 72*x^4 - 164*x^3 + 156*x^2 - 48*x",
"EA]o": "x^6 - 14*x^5 + 73*x^4 - 174*x^3 + 184*x^2 - 66*x",
"EaMw": "x^6 - 16*x^5 + 97*x^4 - 276*x^3 + 364*x^2 - 174*x",
"EBhw": "x^6 - 16*x^5 + 96*x^4 - 264*x^3 + 320*x^2 - 126*x",
"EBjW": "x^6 - 16*x^5 + 97*x^4 - 276*x^3 + 365*x^2 - 180*x",
"EBjw": "x^6 - 18*x^5 + 123*x^4 - 396*x^3 + 595*x^2 - 330*x",
"EImo": "x^6 - 16*x^5 + 98*x^4 - 288*x^3 + 405*x^2 - 216*x",
"EJYW": {
"number": "x^6 - 16*x^5 + 97*x^4 - 274*x^3 + 348*x^2 - 144*x",
"comment": "It has the same Laplacian polynomial as E`NW."
},
"EIno": "x^6 - 18*x^5 + 125*x^4 - 418*x^3 + 672*x^2 - 414*x",
"EImw": "x^6 - 18*x^5 + 124*x^4 - 406*x^3 + 627*x^2 - 360*x",
"EInw": "x^6 - 20*x^5 + 154*x^4 - 568*x^3 + 999*x^2 - 666*x",
"EI]w": "x^6 - 18*x^5 + 123*x^4 - 392*x^3 + 564*x^2 - 270*x",
"EB]w": "x^6 - 18*x^5 + 122*x^4 - 380*x^3 + 523*x^2 - 240*x",
"EB^w": "x^6 - 20*x^5 + 152*x^4 - 538*x^3 + 855*x^2 - 450*x",
"EHuw": "x^6 - 18*x^5 + 124*x^4 - 406*x^3 + 628*x^2 - 366*x",
"EBnW": "x^6 - 18*x^5 + 123*x^4 - 394*x^3 + 585*x^2 - 324*x",
"EBnw": "x^6 - 20*x^5 + 153*x^4 - 554*x^3 + 939*x^2 - 594*x",
"EB~w": "x^6 - 22*x^5 + 187*x^4 - 762*x^3 + 1476*x^2 - 1080*x",
"EFz_": {
"number": "x^6 - 18*x^5 + 126*x^4 - 432*x^3 + 729*x^2 - 486*x",
"comment": "This is the complete bipartite graph $K_{3,3}$."
},
"Es\\w": "x^6 - 20*x^5 + 156*x^4 - 594*x^3 + 1107*x^2 - 810*x",
"EB~o": "x^6 - 20*x^5 + 155*x^4 - 580*x^3 + 1044*x^2 - 720*x",
"EFzw": "x^6 - 22*x^5 + 189*x^4 - 792*x^3 + 1620*x^2 - 1296*x",
"EF~w": "x^6 - 24*x^5 + 225*x^4 - 1026*x^3 + 2268*x^2 - 1944*x",
"EPTW": "x^6 - 14*x^5 + 73*x^4 - 172*x^3 + 172*x^2 - 48*x",
"E`NG": "x^6 - 14*x^5 + 74*x^4 - 180*x^3 + 189*x^2 - 54*x",
"E`NW": {
"number": "x^6 - 16*x^5 + 97*x^4 - 274*x^3 + 348*x^2 - 144*x",
"comment": "It has the same Laplacian polynomial as EJYW."
},
"E`Lw": "x^6 - 16*x^5 + 96*x^4 - 262*x^3 + 304*x^2 - 96*x",
"E`Nw": "x^6 - 18*x^5 + 123*x^4 - 394*x^3 + 576*x^2 - 288*x",
"EJeg": "x^6 - 16*x^5 + 98*x^4 - 284*x^3 + 381*x^2 - 180*x",
"EJqw": "x^6 - 18*x^5 + 125*x^4 - 416*x^3 + 656*x^2 - 384*x",
"EK\\w": "x^6 - 18*x^5 + 123*x^4 - 390*x^3 + 548*x^2 - 240*x",
"EK]w": "x^6 - 18*x^5 + 124*x^4 - 404*x^3 + 611*x^2 - 330*x",
"E`]w": "x^6 - 18*x^5 + 124*x^4 - 404*x^3 + 612*x^2 - 336*x",
"EK^w": "x^6 - 20*x^5 + 154*x^4 - 566*x^3 + 980*x^2 - 624*x",
"EK~o": "x^6 - 20*x^5 + 156*x^4 - 592*x^3 + 1088*x^2 - 768*x",
"EK~w": "x^6 - 22*x^5 + 188*x^4 - 776*x^3 + 1536*x^2 - 1152*x",
"EBn_": "x^6 - 16*x^5 + 98*x^4 - 286*x^3 + 397*x^2 - 210*x",
"E`]o": "x^6 - 16*x^5 + 98*x^4 - 284*x^3 + 384*x^2 - 192*x",
"ELpw": "x^6 - 18*x^5 + 125*x^4 - 416*x^3 + 659*x^2 - 396*x",
"ELrw": {
"number": "x^6 - 20*x^5 + 155*x^4 - 580*x^3 + 1045*x^2 - 726*x",
"comment": "This is the wheel $W_6$."
},
"ELv_": "x^6 - 18*x^5 + 126*x^4 - 428*x^3 + 705*x^2 - 450*x",
"Ek]w": "x^6 - 20*x^5 + 156*x^4 - 592*x^3 + 1091*x^2 - 780*x",
"EJnW": "x^6 - 20*x^5 + 155*x^4 - 578*x^3 + 1027*x^2 - 684*x",
"Ebnw": "x^6 - 22*x^5 + 189*x^4 - 790*x^3 + 1601*x^2 - 1254*x",
"EL~w": "x^6 - 24*x^5 + 226*x^4 - 1040*x^3 + 2328*x^2 - 2016*x",
"ER^W": "x^6 - 20*x^5 + 155*x^4 - 578*x^3 + 1028*x^2 - 690*x",
"EJmw": "x^6 - 20*x^5 + 154*x^4 - 564*x^3 + 965*x^2 - 600*x",
"EJnw": "x^6 - 22*x^5 + 188*x^4 - 774*x^3 + 1517*x^2 - 1110*x",
"EJ]w": "x^6 - 20*x^5 + 153*x^4 - 548*x^3 + 880*x^2 - 450*x",
"EJ^w": "x^6 - 22*x^5 + 186*x^4 - 740*x^3 + 1325*x^2 - 750*x",
"EJ~w": "x^6 - 24*x^5 + 225*x^4 - 1022*x^3 + 2220*x^2 - 1800*x",
"EN~w": "x^6 - 26*x^5 + 267*x^4 - 1350*x^3 + 3348*x^2 - 3240*x",
"EL~o": "x^6 - 22*x^5 + 190*x^4 - 804*x^3 + 1664*x^2 - 1344*x",
"EJ~o": "x^6 - 22*x^5 + 189*x^4 - 788*x^3 + 1580*x^2 - 1200*x",
"Ejmw": "x^6 - 22*x^5 + 190*x^4 - 804*x^3 + 1665*x^2 - 1350*x",
"ENzw": "x^6 - 24*x^5 + 227*x^4 - 1056*x^3 + 2412*x^2 - 2160*x",
"E]~o": "x^6 - 24*x^5 + 228*x^4 - 1072*x^3 + 2496*x^2 - 2304*x",
"E]~w": "x^6 - 26*x^5 + 268*x^4 - 1368*x^3 + 3456*x^2 - 3456*x",
"E^~w": "x^6 - 28*x^5 + 312*x^4 - 1728*x^3 + 4752*x^2 - 5184*x",
"E~~w": {
"number": "x^6 - 30*x^5 + 360*x^4 - 2160*x^3 + 6480*x^2 - 7776*x",
"comment": "This is the complete graph $K_6$."
}
}
},
"T397": {
"title": "Spectral radii of connected graphs",
"numbers": [
"A_",
"BW",
"Bw",
"CF",
"CL",
"CN",
"C]",
"C^",
"C~",
"D?{",
"D@s",
"D@{",
"DIk",
"DBk",
"DB{",
"DFw",
"DF{",
"DBg",
"DK[",
"DK{",
"DLo",
"Dbk",
"DL{",
"DJk",
"DJ{",
"DN{",
"DNw",
"D]{",
"D^{",
"D~{",
"E?Bw",
"E?Fg",
"E?Fw",
"E@FG",
"E?NG",
"E@JW",
"E?NW",
"E?Nw",
"E?]o",
"E?^o",
"E?]w",
"E?^w",
"E?~o",
"E?~w",
"E@QW",
"E@`w",
"E@Rw",
"E@YW",
"EHQW",
"E@UW",
"EGNW",
"EAMw",
"E@Vw",
"E@YO",
"EI_w",
"EGdo",
"EGcw",
"E@ow",
"EK`w",
"ECXw",
"EGdw",
"E_Nw",
"E@NW",
"E@Nw",
"E_]o",
"EENg",
"EC\\w",
"E@^W",
"E_]w",
"E@vw",
"E@^o",
"E@]w",
"E@^w",
"E@~o",
"E@~w",
"EBYW",
"EBYw",
"EBZw",
"EIe_",
"EKNG",
"EHUW",
"EoLW",
"E@]o",
"EA]o",
"EaMw",
"EBhw",
"EBjW",
"EBjw",
"EImo",
"EJYW",
"EIno",
"EImw",
"EInw",
"EI]w",
"EB]w",
"EB^w",
"EHuw",
"EBnW",
"EBnw",
"EB~w",
"EFz_",
"Es\\w",
"EB~o",
"EFzw",
"EF~w",
"EPTW",
"E`NG",
"E`NW",
"E`Lw",
"E`Nw",
"EJeg",
"EJqw",
"EK\\w",
"EK]w",
"E`]w",
"EK^w",
"EK~o",
"EK~w",
"EBn_",
"E`]o",
"ELpw",
"ELrw",
"ELv_",
"Ek]w",
"EJnW",
"Ebnw",
"EL~w",
"ER^W",
"EJmw",
"EJnw",
"EJ]w",
"EJ^w",
"EJ~w",
"EN~w",
"EL~o",
"EJ~o",
"Ejmw",
"ENzw",
"E]~o",
"E]~w",
"E^~w",
"E~~w"
]
},
"T400": {
"title": "Kirchhoff indices of connected graphs",
"numbers": [
"A_",
"BW",
"Bw",
"CF",
"CL",
"CN",
"C]",
"C^",
"C~",
"D?{",
"D@s",
"D@{",
"DIk",
"DBk",
"DB{",
"DFw",
"DF{",
"DBg",
"DK[",
"DK{",
"DLo",
"Dbk",
"DL{",
"DJk",
"DJ{",
"DN{",
"DNw",
"D]{",
"D^{",
"D~{",
"E?Bw",
"E?Fg",
"E?Fw",
"E@FG",
"E?NG",
"E@JW",
"E?NW",
"E?Nw",
"E?]o",
"E?^o",
"E?]w",
"E?^w",
"E?~o",
"E?~w",
"E@QW",
"E@`w",
"E@Rw",
"E@YW",
"EHQW",
"E@UW",
"EGNW",
"EAMw",
"E@Vw",
"E@YO",
"EI_w",
"EGdo",
"EGcw",
"E@ow",
"EK`w",
"ECXw",
"EGdw",
"E_Nw",
"E@NW",
"E@Nw",
"E_]o",
"EENg",
"EC\\w",
"E@^W",
"E_]w",
"E@vw",
"E@^o",
"E@]w",
"E@^w",
"E@~o",
"E@~w",
"EBYW",
"EBYw",
"EBZw",
"EIe_",
"EKNG",
"EHUW",
"EoLW",
"E@]o",
"EA]o",
"EaMw",
"EBhw",
"EBjW",
"EBjw",
"EImo",
"EJYW",
"EIno",
"EImw",
"EInw",
"EI]w",
"EB]w",
"EB^w",
"EHuw",
"EBnW",
"EBnw",
"EB~w",
"EFz_",
"Es\\w",
"EB~o",
"EFzw",
"EF~w",
"EPTW",
"E`NG",
"E`NW",
"E`Lw",
"E`Nw",
"EJeg",
"EJqw",
"EK\\w",
"EK]w",
"E`]w",
"EK^w",
"EK~o",
"EK~w",
"EBn_",
"E`]o",
"ELpw",
"ELrw",
"ELv_",
"Ek]w",
"EJnW",
"Ebnw",
"EL~w",
"ER^W",
"EJmw",
"EJnw",
"EJ]w",
"EJ^w",
"EJ~w",
"EN~w",
"EL~o",
"EJ~o",
"Ejmw",
"ENzw",
"E]~o",
"E]~w",
"E^~w",
"E~~w"
]
},
"T545": {
"title": "Estrada indices of connected graphs",
"numbers": [
"A_",
"BW",
"Bw",
"CF",
"CL",
"CN",
"C]",
"C^",
"C~",
"D?{",
"D@s",
"D@{",
"DBg",
"DBk",
"DB{",
"DFw",
"DF{",
"DIk",
"DJk",
"DJ{",
"DK[",
"DK{",
"DLo",
"DL{",
"DNw",
"DN{",
"D]{",
"D^{",
"Dbk",
"D~{",
"E?Bw",
"E?Fg",
"E?Fw",
"E?NG",
"E?NW",
"E?Nw",
"E?]o",
"E?]w",
"E?^o",
"E?^w",
"E?~o",
"E?~w",
"E@FG",
"E@JW",
"E@NW",
"E@Nw",
"E@QW",
"E@Rw",
"E@UW",
"E@Vw",
"E@YO",
"E@YW",
"E@]o",
"E@]w",
"E@^W",
"E@^o",
"E@^w",
"E@`w",
"E@ow",
"E@vw",
"E@~o",
"E@~w",
"EAMw",
"EA]o",
"EBYW",
"EBYw",
"EBZw",
"EB]w",
"EB^w",
"EBhw",
"EBjW",
"EBjw",
"EBnW",
"EBn_",
"EBnw",
"EB~o",
"EB~w",
"ECXw",
"EC\\w",
"EENg",
"EFz_",
"EFzw",
"EF~w",
"EGNW",
"EGcw",
"EGdo",
"EGdw",
"EHQW",
"EHUW",
"EHuw",
"EI]w",
"EI_w",
"EIe_",
"EImo",
"EImw",
"EIno",
"EInw",
"EJYW",
"EJ]w",
"EJ^w",
"EJeg",
"EJmw",
"EJnW",
"EJnw",
"EJqw",
"EJ~o",
"EJ~w",
"EKNG",
"EK\\w",
"EK]w",
"EK^w",
"EK`w",
"EK~o",
"EK~w",
"ELpw",
"ELrw",
"ELv_",
"EL~o",
"EL~w",
"ENzw",
"EN~w",
"EPTW",
"ER^W",
"E]~o",
"E]~w",
"E^~w",
"E_Nw",
"E_]o",
"E_]w",
"E`Lw",
"E`NG",
"E`NW",
"E`Nw",
"E`]o",
"E`]w",
"EaMw",
"Ebnw",
"Ejmw",
"Ek]w",
"EoLW",
"Es\\w",
"E~~w"
]
},
"T546": {
"title": "Graph energies of connected graphs",
"numbers": {
"A_": {
"number": "2",
"comment": "This is the complete graph $K_{2}$."
},
"BW": {
"number": "2.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145",
"comment": "This is the complete bipartite graph $K_{1,2}$."
},
"Bw": {
"number": "4",
"comment": "This is the complete graph $K_{3}$."
},
"CF": {
"number": "3.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151",
"comment": "This is the complete bipartite graph $K_{1,3}$."
},
"CL": {
"number": "4.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550",
"comment": "This is the path $P_{4}$."
},
"CN": "4.962388608184031245267074482433714361105490433996953456791786281627673844773530106026582365095707850",
"C]": {
"number": "4",
"comment": "This is the complete bipartite graph $K_{2,2}$."
},
"C^": "5.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684297",
"C~": {
"number": "6",
"comment": "This is the complete graph $K_{4}$."
},
"D?{": {
"number": "4",
"comment": "This is the complete bipartite graph $K_{1,4}$."
},
"D@s": "5.226251859505506111426572693708748614335044753397078110195593467632324165844768203807414880770512573",
"D@{": "5.627213005296661630882455124721360484368562409530072110653088354444577673408278880813888259313606972",
"DBg": {
"number": "5.464101615137754587054892683011744733885610507620761256111613958903866033817600074162292373514497151",
"comment": "This is the path $P_{5}$."
},
"DBk": "5.841619252963778989528394936201772181691914933456771936981350301637687873930815344619033490397272993",
"DB{": "6.040895836088439143157393944332025234449332756993754506055066285763845857942823557660177054423363062",
"DFw": {
"number": "4.898979485566356196394568149411782783931894961313340256865385134501920754914630053079718866209280470",
"comment": "This is the complete bipartite graph $K_{2,3}$."
},
"DF{": "6",
"DIk": "5.595865303863626808126162157727995058694090255464955519723745292601494368151921196459313202005787212",
"DJk": "6.729857197628430364684743172119851451390231216405962831133190349826779811483147325378582591321301198",
"DJ{": "7.028273858670582145387549733924434956104952601490809184443342788418683314583547181516140817592433007",
"DK[": "6.428639486755070374830995401697160977815839274438998868662764633018256092866532549591942500683928704",
"DK{": "7.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684297",
"DLo": {
"number": "6.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550",
"comment": "This is the cycle $C_{5}$."
},
"DL{": "7.106932641439849271620054204194994275308998787610094381916855823365030930174096340478767938990008305",
"DNw": "6.354819361798569134901586241832665906713962235605703914510435759821252835127490673103397817754782655",
"DN{": "7.362661287209954750951324775777573098056549906376278871133809559524887491648443547650162111134346972",
"D]{": "6.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550",
"D^{": "7.291502622129181181003231507278520851420518366164900360736668918402137646460567255520785772949087221",
"Dbk": "6.340172973252067445406511528850741850840279259646619907337454812773690100341494779351308368367151965",
"D~{": {
"number": "8",
"comment": "This is the complete graph $K_{5}$."
},
"E?Bw": {
"number": "4.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550",
"comment": "This is the complete bipartite graph $K_{1,5}$."
},
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"E?NG": "6",
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"E?Nw": "6.685846165554340416109718021962283266803071289977970214792795219557662739625068406045771876985518948",
"E?]o": "6.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550",
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"E?^w": "6.892602538996459915510055544713000379505516624355759069718937885622573260677179338179838820195797976",
"E?~o": {
"number": "5.656854249492380195206754896838792314278687501507792292706718951962929913848428155401550137310566291",
"comment": "This is the complete bipartite graph $K_{2,4}$."
},
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"E@FG": "6.155367074350506805140581152073819648013404287075584854078312500749726576990181836909187443334210871",
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"E@Nw": "7.711545013271977351697399500659702416275690538745588800623814926427537724208005134409573773047318314",
"E@QW": "6.898979485566356196394568149411782783931894961313340256865385134501920754914630053079718866209280470",
"E@Rw": "7.806423851823106574970432448114188467550628100088665319208433164164272348434497222916668503955372819",
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"E@Vw": "7.980630624037818356259785136950205553660882817594318091970774715976421647095209526441539773975570397",
"E@YO": {
"number": "6.987918414869868244200039072033918485058197847171216842924395512774829219651898276607540058612682973",
"comment": "This is the path $P_{6}$."
},
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"EBnW": "8.944271909999158785636694674925104941762473438446102897083588981642083702551219597657657633515129100",
"EBn_": "8.138805226879111362292207869575203895224268732804641555922402585705256105953877243733115221389054374",
"EBnw": "8.739132120594849621507374998490704448889330471861664128739367324438100982256889153116876289267583598",
"EB~o": "7.620386170314852043228323625548326198059017885243619916429023858032260593433478290346689734936195818",
"EB~w": "8.584803170449242064607406715328122023224441024878576102185271672630531757157080873495281709748105697",
"ECXw": "7.523338239663346370427019854163306575741281777600115302451214085271832036701569405823716322919619631",
"EC\\w": "7.738308315348773670383805702997256015893208880872407551781541807860154608643026642461734201597656333",
"EENg": "7.299261078610975623914039113910742892221665931773083591908072385707430757083736374533830672717314220",
"EFz_": {
"number": "6",
"comment": "This is the complete bipartite graph $K_{3,3}$."
},
"EFzw": "7.532870967705409570985027514093138426965233756567403282873786952836213690429009296991866816226311875",
"EF~w": "8.324555320336758663997787088865437067439110278650433653715009705585188877278476442688496216758600590",
"EGNW": "7.664074803029532747057158884653540033462970954922327949207832494891403889989321265058799135569028912",
"EGcw": "7.415980409830338533606879652048765431723125679222008151999025725997866846644997402768184860464336890",
"EGdo": "7.549245799008978526396499275838955109331020673056416374699026785931968209056785323729425641799010412",
"EGdw": "7.996110202208088649296548044183282356109804636639527218028460526113526505690393759877014291267753958",
"EHQW": "7.465883060453301293440401790148364171688130886385878141588871469089663331556219585299366100151376852",
"EHUW": "7.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684297",
"EHuw": "8.354510433691246187788401585359558778391570287434694899176055214776519327053007578279328703803712386",
"EI]w": "8.058990926761212908838115834846649501974798530504108716962454683345877715253104825203913712418283488",
"EI_w": "6.602720495543138223533364444482982175157738827615102828121493293368231195114831269210201956142121332",
"EIe_": {
"number": "8",
"comment": "This is the cycle $C_{6}$."
},
"EImo": "6.928203230275509174109785366023489467771221015241522512223227917807732067635200148324584747028994303",
"EImw": "8.046818857603472256363449670096762058722726648012348385626430368601773044836061219778305751385064794",
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"EInw": "8.367008185346933250462298986186914545934939727716523965011213296334176546664038375918551229919433391",
"EJYW": "7.790213031855061353869725602536475764102620319110589315638878498097052329235981808662338895609605228",
"EJ]w": "8.887495848379203243067883913332089078513561870548240015203006509128877100982839912866213975640921379",
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"EJmw": "9.123105625617660549821409855974077025147199225373620434398633573094954346337621593587863650810684297",
"EJnW": "8.761374662616505798953755051538595622962943212525710753837704533664513123196992781931969406533695082",
"EJnw": "9.276221012466257272166994242136815173338707924309142017682447983631636716250095373369971638541906003",
"EJqw": "8.704443792558203844348564992206169557842158505943969604542220567359967330513681795557752191807169533",
"EJ~o": "8.558904631537212739523092317723424403178210058006062496244089250360348058732807645131710872469640256",
"EJ~w": "9.493136493991434602315200217327588875522945350062650619343390089511901699328955007644280581127120015",
"EKNG": "7.656854249492380195206754896838792314278687501507792292706718951962929913848428155401550137310566291",
"EK\\w": "8.707711570861656477116674698043461334364756173301840070083373106868484215602215603448230936081400335",
"EK]w": "8.857845879539719904560491040046454396527738352950486278443571922436654516035091859988808189129889247",
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"EK~w": "9.656854249492380195206754896838792314278687501507792292706718951962929913848428155401550137310566291",
"ELpw": "8.957679683723196469180846030462219229876300364763588355076722450660040818668371691885174680674497794",
"ELrw": "9.371115440565935589212915486874335254813131680536391705407179625322962606190239851908547682966845020",
"ELv_": "8",
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"EL~w": "9.474121328551627543198229735454653111600656048068112031877802560055097191813384324490153379272557755",
"ENzw": "8.858814602077679498235114893473357941217628001603362900070613546266982993360655737824941126813517542",
"EN~w": "9.607084991365190977216903789249965914517164530450806808595762597256895230005584465079200660115220155",
"EPTW": "7.732396525018045010947988461973182812471801511545760923956833409722234152217432395652790061322564501",
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"E]~o": "8",
"E]~w": "8.744562646538028659850611468218929318220264457982792367699877470565900721457404627027125365596788122",
"E^~w": "9.403124237432848686488217674621813264520420132621018885529272626668182758196876074289354302249869963",
"E_Nw": "8.213373930418942300937140671668059228136271707449090014846760917362711189270989274955147776282623690",
"E_]o": "7.564563854420212122516857986342222147547235306566398575893406308353486152439460940160291590543418702",
"E_]w": "7.418550718873845678458263334247781867040053478730873310775911706109062107227028689458838668987775115",
"E`Lw": "8.426782210190877937441515962573110255546985758387040718781980295871188396833727559392869250275773756",
"E`NG": "8.292528739883944684658270131431140891024954258374657402464973434885330990741814151863067442169780297",
"E`NW": "8.698355190948984576147920653150570895697895170588746921672812701273068274726596613790680694577927923",
"E`Nw": "9.203358263766308504928740720375662412400114174479743900804985469463782944844475863965579788572641874",
"E`]o": "8.818643672455629702997220862459284724425074936379497626878139369317389351185575786018775967872227308",
"E`]w": "8.472135954999579392818347337462552470881236719223051448541794490821041851275609798828828816757564550",
"EaMw": "8.182694489906029904975478778099991313301995815079856779410620038593184843719248132354145133606157821",
"Ebnw": "8.978577143620157525585873060909698482336131678965986231073132910341349868285232838686803378771021181",
"Ejmw": "8.828427124746190097603377448419396157139343750753896146353359475981464956924214077700775068655283145",
"Ek]w": "8.755422416913548648976315770728372961290390146882261791084206989648956280090617007302950962310014388",
"EoLW": "8.389762986525928263657805858015282898065057334380609371575904559128536166110804118691284157147071123",
"Es\\w": "7.435482234928008190257458925909355675319276537159085057594381136795997924564337448889409938510939521",
"E~~w": {
"number": "10",
"comment": "This is the complete graph $K_{6}$."
}
}
},
"T547": {
"title": "Algebraic connectivity of connected graphs",
"numbers": [
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"BW",
"Bw",
"CF",
"CL",
"CN",
"C]",
"C^",
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"E~~w"
]
}
}