Universal Tutte and Reduced Polynomials

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

Graph Polynomials and Their Applications I: The Tutte Polynomial

We begin our exploration of graph polynomials and their applications with the Tutte polynomial, a renown tool for analyzing properties of graphs and networks. This two-variable graph polynomial, due to W. T. Tutte [Tut47,Tut54, Tut67], has the important universal property that essentially any multiplicative graph invariant with a deletion/contraction reduction must be an evaluation of it. These...

Semimatroids and their Tutte polynomials

We define and study semimatroids, a class of objects which abstracts the dependence properties of an affine hyperplane arrangement. We show that geometric semilattices are precisely the posets of flats of semimatroids. We define and investigate the Tutte polynomial of a semimatroid. We prove that it is the universal Tutte-Grothendieck invariant for semimatroids, and we give a combinatorial inte...

Polynomial Tutte Invariants of Rooted Integral Gain Graphs

We present dichromatic and tree-expansion polynomials of integral gain graphs that underlie the problem of counting lattice points in the complement of an integral affinographic hyperplane arrangement. This is a step towards finding the universal Tutte invariant of rooted integral gain graphs. Mathematics Subject Classifications (2000): Primary 05C22; Secondary 05C15.