The notion of graph polynomials definable in Monadic Second Order Logic, MSOL, was introduced in [Mak04]. It was shown that the Tutte polynomial and its generalization, as well as the matching polynomial, the cover polynomial and the various interlace polynomials fall into this category. In this paper we present a framework of graph polynomials based on counting functions of generalized colorin...

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...

We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of Tutte polynomial. As an application, generalization golden identity is proved for graphs on torus.

Abstract. This paper deals with the partition function of the Ising model from statistical mechanics, which is used to study phase transitions in physical systems. A special case of interest is that of the Ising model with constant energies and external field. One may consider such an Ising system as a simple graph together with vertex and edge weights. When these weights are considered indeter...