Tutte Polynomials and Graph Symmetries

The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures i...

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Bibliographic Details
Published in:	Symmetry (Basel) Vol. 14; no. 10; p. 2072
Main Authors:	Chbili, Nafaa, Alderai, Noura, Ali, Roba, AlQedra, Raghd
Format:	Journal Article
Language:	English
Published:	Basel MDPI AG 01-10-2022
Subjects:	automorphism group Automorphisms Euclidean space Graphs Ising model Isomorphism Knot theory Polynomials Symmetry Tutte polynomial
Online Access:	Get full text
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Summary:	The Tutte polynomial is an isomorphism invariant of graphs that generalizes the chromatic and the flow polynomials. This two-variable polynomial with integral coefficients is known to carry important information about the properties of the graph. It has been used to prove long-standing conjectures in knot theory. Furthermore, it is related to the Potts and Ising models in statistical physics. The purpose of this paper is to study the interaction between the Tutte polynomial and graph symmetries. More precisely, we prove that if the automorphism group of the graph G contains an element of prime order p, then the coefficients of the Tutte polynomial of G satisfy certain necessary conditions.
ISSN:	2073-8994 2073-8994
DOI:	10.3390/sym14102072