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