Exact Potts/Tutte Polynomials for Polygon Chain Graphs

TL;DR

This paper provides exact calculations of Potts model partition functions and Tutte polynomials for polygon chain graphs, offering insights into related graph invariants and special cases like flow and reliability polynomials.

Contribution

It introduces exact formulas for Potts and Tutte polynomials for polygon chain graphs with different boundary conditions, expanding analytical tools in graph theory and statistical physics.

Findings

Exact Potts partition functions derived for polygon chain graphs.

Tutte polynomials computed for various boundary conditions.

Connections to flow and reliability polynomials discussed.

Abstract

We present exact calculations of Potts model partition functions and the equivalent Tutte polynomials for polygon chain graphs with open and cyclic boundary conditions. Special cases of the results that yield flow and reliability polynomials are discussed. We also analyze special cases of the Tutte polynomials that determine various quantities of graph-theoretic interest.