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Teoreticheskaya i Matematicheskaya Fizika, 2021, Volume 207, Number 2, Pages 226–236
DOI: https://doi.org/10.4213/tmf10034 (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
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DOI: https://doi.org/10.4213/tmf10034
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.
Funding agency Grant number
Russian Science Foundation 20-71-10110
This research was supported by a grant from the Russian Science Foundation (Project No. 20-71-10110).
Received: 14.12.2020
Revised: 14.12.2020
English version:
Theoretical and Mathematical Physics, 2021, Volume 207, Issue 2, Pages 594–603
DOI: https://doi.org/10.1134/S0040577921050056
Bibliographic databases:
Document Type: Article
MSC: 05С31, 20J06
Language: Russian
Citation: B. S. Bychkov, A. A. Kazakov, D. V. Talalaev, “Tutte polynomials of vertex-weighted graphs and group cohomology”, TMF, 207:2 (2021), 226–236; Theoret. and Math. Phys., 207:2 (2021), 594–603
Citation in format AMSBIB
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\jour Theoret. and Math. Phys.
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\crossref{https://doi.org/10.1134/S0040577921050056}
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  • https://www.mathnet.ru/eng/tmf/v207/i2/p226
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    		Теоретическая и математическая физика Theoretical and Mathematical Physics
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