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Tutte polynomials of vertex-weighted graphs and group cohomology

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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.

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Funding

This research was supported by a grant from the Russian Science Foundation (Project No. 20-71-10110).

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Authors and Affiliations

  1. Centre of Integrable Systems, Demidov Yaroslavl State University, Yaroslavl, Russia

    B. S. Bychkov, A. A. Kazakov & D. V. Talalaev

  2. National Research University Higher School of Economics, Moscow, Russia

    B. S. Bychkov

Authors
  1. B. S. Bychkov
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  2. A. A. Kazakov
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  3. D. V. Talalaev
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Correspondence to B. S. Bychkov.

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The authors declare no conflicts of interest.

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Translated from Teoreticheskaya i Matematicheskaya Fizika, 2021, Vol. 207, pp. 226-236 https://doi.org/10.4213/tmf10034.

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Bychkov, B.S., Kazakov, A.A. & Talalaev, D.V. Tutte polynomials of vertex-weighted graphs and group cohomology. Theor Math Phys 207, 594–603 (2021). https://doi.org/10.1134/S0040577921050056

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  • DOI: https://doi.org/10.1134/S0040577921050056

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