Tutte Polynomials and Graph Symmetries

Nafaa Chbili, Noura Alderai, Roba Ali, Raghd AlQedra

Research output: Contribution to journalArticlepeer-review

Abstract

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.

Original languageEnglish
Article number2072
JournalSymmetry
Volume14
Issue number10
DOIs
Publication statusPublished - Oct 2022

Keywords

  • Tutte polynomial
  • automorphism group
  • graphs
  • symmetry

ASJC Scopus subject areas

  • Computer Science (miscellaneous)
  • Chemistry (miscellaneous)
  • Mathematics(all)
  • Physics and Astronomy (miscellaneous)

Fingerprint

Dive into the research topics of 'Tutte Polynomials and Graph Symmetries'. Together they form a unique fingerprint.

Cite this