Chain polynomials and Tutte polynomials

Tutte Polynomials of Flower Graphs

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 hyperplane arrangements and the finite field method

The Tutte polynomial is a fundamental invariant associated to a graph, matroid, vector arrangement, or hyperplane arrangement, which answers a wide variety of questions about its underlying object. This short survey focuses on some of the most important results on Tutte polynomials of hyperplane arrangements. We show that many enumerative, algebraic, geometric, and topological invariants of a h...

Tutte Polynomials of Signed Graphs and Jones Polynomials of Some Large Knots

It is well-known that the Jones polynomial of a knot is closely related to the Tutte polynomial of a special graph obtained from a regular projection of the knot. In this paper, we study the Tutte polynomials for signed graphs. We show that if a signed graph is constructed from a simpler graph via k-thickening or k-stretching, then its Tutte polynomial can be expressed in terms of the Tutte pol...

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...