Graph polynomials and symmetries
2019 ◽
Vol 18
(09)
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pp. 1950172
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In a recent paper, we studied the interaction between the automorphism group of a graph and its Tutte polynomial. More precisely, we proved that certain symmetries of graphs are clearly reflected by their Tutte polynomials. The purpose of this paper is to extend this study to other graph polynomials. In particular, we prove that if a graph [Formula: see text] has a symmetry of prime order [Formula: see text], then its characteristic polynomial, with coefficients in the finite field [Formula: see text], is determined by the characteristic polynomial of its quotient graph [Formula: see text]. Similar results are also proved for some generalization of the Tutte polynomial.
2010 ◽
Vol DMTCS Proceedings vol. AN,...
(Proceedings)
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2000 ◽
Vol 9
(4)
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pp. 363-367
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2020 ◽
Vol 12
(02)
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pp. 2050017
Keyword(s):
2014 ◽
Vol 07
(01)
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pp. 1450001
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Keyword(s):
2019 ◽
Vol 169
(2)
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pp. 255-297
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Keyword(s):
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