The Tutte polynomial for homeomorphism classes of graphs

Tutte Polynomials of Flower Graphs

Tutte polynomial expansions for 2-separable graphs

Let Ĝ be a graph obtained from a graph G with no loops or coloops by replacing each edge e= uw of G by a connected graph He that has only the vertices u and w in common with the rest of Ĝ. Two mutually dual formulas are proved for the Tutte polynomial of Ĝ in terms of parameters of the graphs He and (in the one case) 0ow polynomials of subgraphs of G or (in the other case) tension polynomials o...

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.

Parametrized Tutte Polynomials of Graphs and Matroids

We generalize and unify results on parametrized and coloured Tutte polynomials of graphs and matroids due to Zaslavsky, and Bollobás and Riordan. We give a generalized Zaslavsky– Bollobás–Riordan theorem that characterizes parametrized contraction–deletion functions on minor-closed classes of matroids, as well as the modifications necessary to apply the discussion to classes of graphs. In gener...