Generalized star configurations and the Tutte polynomial

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.

On the tutte polynomial of benzenoid chains

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

The Tutte Polynomial as a Growth Function

The ‘dollar game’ represents a kind of diffusion process on a graph. Under the rules of the game some configurations are both stable and recurrent, and these are known as critical configurations. The set of critical configurations can be given the structure of an abelian group, and it turns out that the order of the group is the tree-number of the graph. Each critical configuration can be assig...

Generalized activities and the tutte polynomial

The notion of activities with respect to spanning trees in graphs was introduced by W.T. Tutte, and generalized to activities with respect to bases in matroids by H. Crapo. We present a further generalization, to activities with respect to arbitrary subsets of matroids. These generalized activities provide a unified view of several different expansions of the Tutte polynomial and the chromatic ...

Tutte Polynomials of Flower Graphs