Tutte-martin polynomials and orienting vectors of isotropic systems

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 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.

Tutte Polynomials of Flower Graphs

Isotropic systems and the interlace polynomial

Through a series of papers in the 1980’s, Bouchet introduced isotropic systems and the Tutte-Martin polynomial of an isotropic system. Then, Arratia, Bollobás, and Sorkin developed the interlace polynomial of a graph in [ABS00] in response to a DNA sequencing application. The interlace polynomial has generated considerable recent attention, with new results including realizing the original inte...

The Circuit Partition Polynomial with Applications and Relation to the Tutte and Interlace Polynomials

This paper examines several polynomials related to the field of graph theory including the circuit partition polynomial, Tutte polynomial, and the interlace polynomial. We begin by explaining terminology and concepts that will be needed to understand the major results of the paper. Next, we focus on the circuit partition polynomial and its equivalent, the Martin polynomial. We examine the resul...