Exact Potts/Tutte Polynomials for Polygon Chain Graphs

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.

16 pages, latex, 1 figure

References in corpus (6)

• Exact Potts Model Partition Functions on Ladder Graphs
• Exact Potts Model Partition Functions on Wider Arbitrary-Length Strips of the Square Lattice
• Exact Potts Model Partition Function on Strips of the Triangular Lattice
• Exact Potts Model Partition Function for Strips of the Square Lattice
• Ground State Entropy of Potts Antiferromagnets on Cyclic Polygon Chain Graphs
• Reliability Polynomials and their Asymptotic Limits for Families of Graphs

Cited by in corpus (3)

• Tutte polynomial of pseudofractal scale-free web
• The Structure of Chromatic Polynomials of Planar Triangulation Graphs and Implications for Chromatic Zeros and Asymptotic Limiting Quantities
• Exact Potts/Tutte Polynomials for Hammock Chain Graphs