Generalized activities 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.

Generalized activities and reliability

The analysis of the Tutte polynomial of a matroid using activities is associated with a shelling of the family of spanning sets. We introduce an activities analysis of the reliability of a system specified by an arbitrary clutter, associated with an S-partition rather than a shelling. These activities are related to a method of constructing Boolean interval partitions developed by Dawson in the...

Generalize activities and -terminal relia

Traldi, L., Generalized activities and K-terminal reliability, Discrete Mathematics 96 (1991) 131-149. Suppose each edge of a graph G has a given probability of being useable, and suppose K is some subset of the vertex-set of G. We present a polynomial that is useful in assessing the probability that the elements of K will lie in a particular number of components of the useable portion of G. th...

Tutte Polynomials of Flower Graphs