Polynomials related to chromatic polynomials

Abstract

For a simple graph G, let χ(G, x) denote the chromatic polynomial of G. This manuscript introduces some polynomials which are related to chromatic polynomial and their relations. Contents 1 The Potts model partition function 2 Tutte polynomial T G (x, y) 3 Characteristic polynomial of a matroid 4 Flow polynomial F (G, x) 5 Order polynomial Ω(D, x) 6 Express χ(G, x) in terms of Ω(D, x) 7 σ-polynomial σ(G, x) 8 w-polynomial w(G, x) 9 τ -polynomial τ (G, x)