Tutte polynomials for trees

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

Computing the Tutte polynomial of a hyperplane arrangement

We define and study the Tutte polynomial of a hyperplane arrangement. We introduce a method for computing it by solving an enumerative problem in a finite field. For specific arrangements, the computation of Tutte polynomials is then reduced to certain related enumerative questions. As a consequence, we obtain new formulas for the generating functions enumerating alternating trees, labelled tre...

Tutte Polynomials and Related Asymptotic Limiting Functions for Recursive Families of Graphs

We prove several theorems concerning Tutte polynomials T (G, x, y) for recursive families of graphs. In addition to its interest in mathematics, the Tutte polynomial is equivalent to an important function in statistical physics, the Potts model partition function of the q-state Potts model, Z(G, q, v), where v is a temperature-dependent variable. We determine the structure of the Tutte polynomi...

Visualising the Tutte Polynomial Computation

The Tutte polynomial is an important concept in graph theory which captures many important properties of graphs (e.g. chromatic number, number of spanning trees etc). It also provides a normalised representation that can be used as an equivalence relation on graphs and has applications in diverse areas such micro-biology and physics. A highly efficient algorithm for computing Tutte polynomials ...