The Tutte polynomial was defined originally for graphs and extends to more generally to matroids. The many natural combinatorial interpretations of its evaluations and coefficients for graphs then translate to not obviously related combinatorial quantities in other matroids. For example, the Tutte polynomial evaluated at (2, 0) gives the number of acyclic orientations of a graph. Zaslavsky prov...

Many combinatorial and topological invariants of a hyperplane arrangement can be computed in terms of its Tutte polynomial. Similarly, many invariants of a hypertoric arrangement can be computed in terms of its arithmetic Tutte polynomial. We compute the arithmetic Tutte polynomials of the classical root systems An, Bn, Cn, and Dn with respect to their integer, root, and weight lattices. We do ...

It is known that a certain case of the all-terminal network reliability can be computed via the Tutte polynomial which is an invariant in graph theory. Recently, we have proposed a new approach of computing the Tutte polynomial of a graph of moderate size [9]. In this paper, by using it we analyze computation method of the general all-terminal network reliability and two-terminal network reliab...

We derive a formula for the Tutte polynomial t(G′; x, y) of a q-cone G′ of a GF (q)-representable geometry G in terms of t(G; x, y). We use this to construct collections of infinite sequences of GF (q)-representable geometries in which corresponding geometries are not isomorphic and yet have the same Tutte polynomial. We also use this to construct, for each positive integer k, sets of non-isomo...

This paper initiates a study of the connection between graph homomorphisms and the Tutte polynomial. This connection enables us to extend the study to other important polynomial invariants associated with graphs, and closely related to the Tutte polynomial. We then obtain applications of these relationships in several areas, including Abelian Groups and Statistical Physics. A new type of unique...

A graph polynomial q(G; ) has recently been studied byArratia et al. [The interlace polynomial: a new graph polynomial, in: Proceedings of the EleventhAnnual ACM-SIAM Symposium on Discrete Mathematics, San Francisco, CA, 2000, North-Holland, Amsterdam, pp. 237–245]. That polynomial can be derived from the restricted Tutte–Martin polynomial of an isotropic system, which we introduced [A. Bouchet...

The celebrated Thistlethwaite theorem relates the Jones polynomial of a link with the Tutte polynomial of the corresponding planar graph. We give a generalization of this theorem to virtual links. In this case, the graph will be embedded into a (higher genus) surface. For such graphs we use the generalization of the Tutte polynomial discovered by B. Bollobás and O. Riordan.

The Tutte polynomial of a graph is a 2-variable polynomial which is quite important in both combinatorics and statistical physics. It contains various numerical invariants and polynomial invariants ,such as the number of spanning trees,the number of spanning forests , the number of acyclic orientations , the reliability polynomial,chromatic polynomial and flow polynomial . In this paper,we stud...