Tutte polynomial of some multigraphs

Abstract

Using two related parameters, ζ and γ, we extend the recursion for computing the Tutte polynomial of any graph to the computation of the Tutte polynomial of any multigraph. With this recursion, we found explicit formulae for several families of multigraphs. In particular, the Tutte polynomials of some cyclic multigraphs, 2−tree  multigraphs, and any l−bridge multigraph.

Keywords: Tutte polynomial, multigraph, multi-bridge, 2-tree, fan.