Tutte polynomials of q-cones

Tutte Polynomials of Flower Graphs

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.

Lattice path matroids: enumerative aspects and Tutte polynomials

Fix two lattice paths P and Q from ð0; 0Þ to ðm; rÞ that use East and North steps with P never going above Q: We show that the lattice paths that go from ð0; 0Þ to ðm; rÞ and that remain in the region bounded by P and Q can be identified with the bases of a particular type of transversal matroid, which we call a lattice path matroid. We consider a variety of enumerative aspects of these matroid...

Graph polynomials derived from Tutte-Martin polynomials

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...

Tutte Polynomials and Related Asymptotic Limiting Functions for Recursive Families of Graphs

We prove several theorems concerning Tutte polynomials T (G, x, y) for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important function in statistical physics, the Potts model partition function of the q-state Potts model, Z(G, q, v), where v is a temperature-dependent variable. We determine the structure of the Tutte polynomi...