Tutte Polynomials for Directed Graphs

Tutte Polynomials of Flower Graphs

Chromatic and tension polynomials of graphs

Abstract. This is the first one of a series of papers on association of orientations, lattice polytopes, and abelian group arrangements to graphs. The purpose is to interpret the integral and modular tension polynomials of graphs at zero and negative integers. The whole exposition is put under the framework of subgroup arrangements and the application of Ehrhart polynomials. Such viewpoint lead...

Tutte polynomials of wheels via generating functions

We find an explicit expression of the Tutte polynomial of an $n$-fan. We also find a formula of the Tutte polynomial of an $n$-wheel in terms of the Tutte polynomial of $n$-fans. Finally, we give an alternative expression of the Tutte polynomial of an $n$-wheel and then prove the explicit formula for the Tutte polynomial of an $n$-wheel.

Tutte Polynomials and Related Asymptotic Limiting Functions for Recursive Families of Graphs

We prove several theorems concerning Tutte polynomials T (G, x, y) for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important function in statistical physics, the Potts model partition function of the q-state Potts model, Z(G, q, v), where v is a temperature-dependent variable. We determine the structure of the Tutte polynomi...

On the Cover Polynomial of a Digraph

There are many polynomials which can be associated with a graph G, the most well known perhaps being the Tutte polynomial T (G; x, y) (cf. [B74] or [T54]). In particular, for specific values of x and y, T (G; x, y) enumerates various features of G. For example, T (G; 1, 1) is just the number of spanning trees of G, T (G; 2, 0) is the number of acyclic orientations of G, T (G; 1, 2) is the numbe...