The Tutte polynomial of a class of compound graphs and its applications

Abstract

The Tutte polynomial, a considerable generalization of the chromatic polynomial, associated with a graph is a classical bivariate polynomial, which gives various interesting information about the graph structure. In this paper, we first present a formula for the Tutte polynomial of a class of special compound graphs. Then as applications, we obtain the Tutte polynomials of some complex network models in the context of statistical physics and the Tutte polynomials of some chemical polycyclic graphs. Moreover, explicit expressions of the number of spanning trees for these considered graphs are determined, respectively.