History of Tutte polynomials of connected graphs

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when	who	what
2026-08-28 15:02	bmatschke with claude-opus-5	the names of the graphs that have one	current reviewed
2026-08-28 15:00	bmatschke	Tutte polynomials of every connected graph on at most seven vertices
2026-08-28 15:00	bmatschke with claude-opus-5	proposed from tutte.yaml

What changed between 2026-08-28 15:00 and 2026-08-28 15:02

from line 58 (25 lines, 6 more than before) @@ -58,19 +58,25 @@

     g: '@'   number: '1'+  comment: complete graph $K_1$ - params:     g: A_   number: x+  comment: complete graph $K_2$ - params:     g: BW   number: x^2+  comment: path $P_3$ - params:     g: Bw   number: x^2 + x + y+  comment: complete graph $K_3$ - params:     g: CF   number: x^3+  comment: star $K_{1,3}$ - params:     g: CL   number: x^3+  comment: path $P_4$ - params:     g: CN

from line 85 (17 lines, 4 more than before) @@ -79,13 +85,17 @@

     g: C]   number: x^3 + x^2 + x + y+  comment: cycle $C_4$ - params:     g: C^   number: x^3 + 2*x^2 + 2*x*y + y^2 + x + y+  comment: diamond graph - params:     g: C~   number: x^3 + y^3 + 3*x^2 + 4*x*y + 3*y^2 + 2*x + 2*y+  comment: complete graph $K_4$ - params:     g: D?{   number: x^4+  comment: star $K_{1,4}$ - params:     g: D@s

from line 110 (13 lines, 3 more than before) @@ -100,10 +110,13 @@

     g: DBk   number: x^4 + x^3 + x^2*y+  comment: bull graph - params:     g: DB{   number: x^4 + 2*x^3 + 2*x^2*y + x*y^2 + x^2 + x*y+  comment: dart graph - params:     g: DFw   number: x^4 + 2*x^3 + 3*x^2 + 3*x*y + y^2 + x + y+  comment: complete bipartite graph $K_{2,3}$ - params:     g: DF{

from line 125 (5 lines, 1 more than before) @@ -112,4 +125,5 @@

     g: DBg   number: x^4+  comment: path $P_5$ - params:     g: DK[

from line 132 (13 lines, 3 more than before) @@ -118,10 +132,13 @@

     g: DK{   number: x^4 + 2*x^3 + 2*x^2*y + x^2 + 2*x*y + y^2+  comment: butterfly graph - params:     g: DLo   number: x^4 + x^3 + x^2 + x + y+  comment: cycle $C_5$ - params:     g: Dbk   number: x^4 + 2*x^3 + x^2*y + 2*x^2 + 2*x*y + y^2 + x + y+  comment: house graph - params:     g: DL{

from line 154 (5 lines, 1 more than before) @@ -137,4 +154,5 @@

   number: x^4 + x*y^3 + y^4 + 4*x^3 + 5*x^2*y + 5*x*y^2 + 3*y^3 + 5*x^2 + 7*x*y +     4*y^2 + 2*x + 2*y+  comment: house X graph - params:     g: DNw

from line 162 (5 lines, 1 more than before) @@ -144,4 +162,5 @@

   number: x^4 + y^4 + 4*x^3 + 4*x^2*y + 4*x*y^2 + 4*y^3 + 6*x^2 + 9*x*y + 6*y^2 +     3*x + 3*y+  comment: wheel $W_4$ - params:     g: D^{

from line 171 (9 lines, 2 more than before) @@ -152,7 +171,9 @@

   number: y^6 + 4*y^5 + x^4 + 5*x*y^3 + 10*y^4 + 6*x^3 + 10*x^2*y + 15*x*y^2 + 15*y^3     + 11*x^2 + 20*x*y + 15*y^2 + 6*x + 6*y+  comment: complete graph $K_5$ - params:     g: E?Bw   number: x^5+  comment: star $K_{1,5}$ - params:     g: E?Fg

from line 214 (5 lines, 1 more than before) @@ -193,4 +214,5 @@

   number: x^5 + 3*x^4 + 6*x^3 + 6*x^2*y + 4*x*y^2 + y^3 + 4*x^2 + 4*x*y + y^2 + x     + y+  comment: complete bipartite graph $K_{2,4}$ - params:     g: E?~w

from line 250 (5 lines, 1 more than before) @@ -228,4 +250,5 @@

     g: E@YO   number: x^5+  comment: path $P_6$ - params:     g: EI_w

from line 338 (5 lines, 1 more than before) @@ -315,4 +338,5 @@

     g: EIe_   number: x^5 + x^4 + x^3 + x^2 + x + y+  comment: cycle $C_6$ - params:     g: EKNG

from line 423 (5 lines, 1 more than before) @@ -399,4 +423,5 @@

   number: x^5 + 4*x^4 + y^4 + 10*x^3 + 9*x^2*y + 6*x*y^2 + 5*y^3 + 11*x^2 + 15*x*y     + 9*y^2 + 5*x + 5*y+  comment: complete bipartite graph $K_{3,3}$ - params:     g: Es\w

from line 507 (5 lines, 1 more than before) @@ -482,4 +507,5 @@

   number: x^5 + y^5 + 5*x^4 + 5*x^3*y + 5*x^2*y^2 + 5*x*y^3 + 5*y^4 + 10*x^3 + 15*x^2*y     + 15*x*y^2 + 10*y^3 + 10*x^2 + 16*x*y + 10*y^2 + 4*x + 4*y+  comment: wheel $W_5$ - params:     g: ELv_

from line 600 (9 lines, 2 more than before) @@ -574,7 +600,9 @@

     + 60*x*y^4 + 96*y^5 + 10*x^4 + 20*x^3*y + 45*x^2*y^2 + 105*x*y^3 + 120*y^4 + 35*x^3     + 90*x^2*y + 145*x*y^2 + 120*y^3 + 50*x^2 + 106*x*y + 80*y^2 + 24*x + 24*y+  comment: complete graph $K_6$ - params:     g: F??Fw   number: x^6+  comment: star $K_{1,6}$ - params:     g: F??Ng

from line 664 (5 lines, 1 more than before) @@ -636,4 +664,5 @@

   number: x^6 + 4*x^5 + 10*x^4 + 10*x^3*y + 10*x^2*y^2 + 5*x*y^3 + y^4 + 10*x^3 +     10*x^2*y + 5*x*y^2 + y^3 + 5*x^2 + 5*x*y + y^2 + x + y+  comment: complete bipartite graph $K_{2,5}$ - params:     g: F?B~w

from line 1421 (5 lines, 1 more than before) @@ -1392,4 +1421,5 @@

     + 17*y^4 + 38*x^3 + 54*x^2*y + 51*x*y^2 + 29*y^3 + 36*x^2 + 53*x*y + 30*y^2 +     13*x + 13*y+  comment: complete bipartite graph $K_{3,4}$ - params:     g: F?~vg

from line 1461 (5 lines, 1 more than before) @@ -1431,4 +1461,5 @@

     g: F@HSO   number: x^6+  comment: path $P_7$ - params:     g: F@O\G

from line 1746 (5 lines, 1 more than before) @@ -1715,4 +1746,5 @@

     g: FHQSO   number: x^6 + x^5 + x^4 + x^3 + x^2 + x + y+  comment: cycle $C_7$ - params:     g: FGSkg

from line 3234 (5 lines, 1 more than before) @@ -3202,4 +3234,5 @@

     15*x^4 + 24*x^3*y + 27*x^2*y^2 + 24*x*y^3 + 15*y^4 + 20*x^3 + 36*x^2*y + 36*x*y^2     + 20*y^3 + 15*x^2 + 25*x*y + 15*y^2 + 5*x + 5*y+  comment: wheel $W_6$ - params:     g: FHo}g

from line 3998 (5 lines, 1 more than before) @@ -3965,4 +3998,5 @@

     + 8*x*y^3 + 6*y^4 + 15*x^3 + 26*x^2*y + 24*x*y^2 + 13*y^3 + 12*x^2 + 20*x*y +     12*y^2 + 4*x + 4*y+  comment: Moser spindle - params:     g: FKLkw

from line 4657 (3 lines, 1 more than before) @@ -4623,2 +4657,3 @@

     + 1330*x*y^3 + 1225*y^4 + 225*x^3 + 721*x^2*y + 1225*x*y^2 + 945*y^3 + 274*x^2     + 644*x*y + 490*y^2 + 120*x + 120*y+  comment: complete graph $K_7$