Geodesic
Tutte polynomials of vertex-weighted graphs and group cohomology
Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 226-236

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We construct a generalization of the Tutte polynomial for vertex-weighted graphs for which the coefficients of the “deletion–contraction” relation depend nontrivially on the vertex weights. We show that the corresponding relation on the coefficients coincides with the two-cocycle relation in the group cohomology. We obtain a representation of a new invariant by summing over subgraphs and establish its connection with four-invariants of graphs.
Mots-clés : Tutte polynomial
Keywords: group cohomology. 
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     author = {B. S. Bychkov and A. A. Kazakov and D. V. Talalaev},
     title = {Tutte polynomials of vertex-weighted graphs and group cohomology},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {226--236},
     publisher = {mathdoc},
     volume = {207},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a4/}
}
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B. S. Bychkov; A. A. Kazakov; D. V. Talalaev. Tutte polynomials of vertex-weighted graphs and group cohomology. Teoretičeskaâ i matematičeskaâ fizika, Tome 207 (2021) no. 2, pp. 226-236. http://geodesic.mathdoc.fr/item/TMF_2021_207_2_a4/