Graph polynomials derived from Tutte-Martin polynomials

Tutte Polynomials of Flower Graphs

Identities for circuit partition polynomials , with applications to the Tutte polynomial

The Martin polynomials, introduced by Martin in his 1977 thesis, encode information about the families of circuits in Eulerian graphs and digraphs. The circuit partition polynomials, J (G;x) and j ( G;x), are simple transformations of the Martin polynomials. We give new identities for these polynomials, analogous to Tutte’s identity for the chromatic polynomial. Following a useful expansion of ...

The Circuit Partition Polynomial with Applications and Relation to the Tutte and Interlace Polynomials

This paper examines several polynomials related to the field of graph theory including the circuit partition polynomial, Tutte polynomial, and the interlace polynomial. We begin by explaining terminology and concepts that will be needed to understand the major results of the paper. Next, we focus on the circuit partition polynomial and its equivalent, the Martin polynomial. We examine the resul...

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 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...