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TMF, 2021 Volume 207, Number 2, Pages 226–236 (Mi tmf10034)

Tutte polynomials of vertex-weighted graphs and group cohomology

B. S. Bychkovab, A. A. Kazakova, D. V. Talalaeva

a Centre of integrable systems,Demidov Yaroslavl State University, Yaroslavl, Russia
b National Research University "Higher School of Economics", Moscow, Russia

Abstract: 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.

Keywords: Tutte polynomial, group cohomology.

MSC: 05Ñ31, 20J06

Received: 14.12.2020
Revised: 14.12.2020

DOI: 10.4213/tmf10034


 English version:
Theoretical and Mathematical Physics, 2021, 207:2, 594–603

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© Steklov Math. Inst. of RAS, 2024