An Interpretation for the Tutte Polynomial

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.

On the tutte polynomial of benzenoid chains

The Tutte polynomial of a graph G, T(G, x,y) is a polynomial in two variables defined for every undirected graph contains information about how the graph is connected. In this paper a simple formula for computing Tutte polynomial of a benzenoid chain is presented.

Tutte Polynomials of Flower Graphs

The multivariate arithmetic Tutte polynomial

We introduce an arithmetic version of the multivariate Tutte polynomial recently studied by Sokal, and a quasi-polynomial that interpolates between the two. We provide a generalized Fortuin-Kasteleyn representation for representable arithmetic matroids, with applications to arithmetic colorings and flows. We give a new proof of the positivity of the coefficients of the arithmetic Tutte polynomi...

Ehrhart theory, modular flow reciprocity, and the Tutte polynomial

Given an oriented graph G, the modular flow polynomial φG(k) counts the number of nowhere-zero Zk-flows of G. We give a description of the modular flow polynomial in terms of (open) Ehrhart polynomials of lattice polytopes. Using Ehrhart–Macdonald reciprocity we give a combinatorial interpretation for the values of φG at negative arguments which answers a question of Beck and Zaslavsky (Adv Mat...