Computing the Tutte polynomial of Archimedean tilings

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.

Tilings of rectangles with T-tetrominoes

We prove that any two tilings of a rectangular region by T-tetrominoes are connected by moves involving only 2 and 4 tiles. We also show that the number of such tilings is an evaluation of the Tutte polynomial. The results are extended to a more general class of regions.

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.

Combinatorial evaluations of the Tutte polynomial

The Tutte polynomial is one of the most important and most useful invariants of a graph. It was discovered as a two variable generalization of the chromatic polynomial [15, 16], and has been studied in literally hundreds of papers, in part due to its connections to various fields ranging from Enumerative Combinatorics to Knot Theory, from Statistical Physics to Computer Science. We refer the re...

Tutte Polynomials of Flower Graphs