tutte polynomials of wheels via generating functions

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

Generating Functions of Jacobi Polynomials

Multiplicative renormalization method (MRM) for deriving generating functions of orthogonal polynomials is introduced by Asai–Kubo– Kuo. They and Namli gave complete lists of MRM-applicable measures for MRM-factors h(x) = ex and (1 − x)−κ. In this paper, MRM-factors h(x) for which the beta distribution B(p, q) over [0, 1] is MRM-applicable are determined. In other words, all generating function...

Chain polynomials and Tutte polynomials

The recently introduced chain and sheaf polynomials of a graph are shown to be essentially equivalent to a weighted version of the Tutte polynomial. c © 2002 Elsevier Science B.V. All rights reserved.

Tutte Polynomials

Let ∆ be a finite sequence of n vectors from a vector space over any field. We consider the subspace of Sym(V) spanned by Q v∈S v, where S is a subsequence of ∆. A result of Orlik and Terao provides a doubly indexed direct sum of this space. The main theorem is that the resulting Hilbert series is the Tutte polynomial evaluation T (∆; 1 + x, y). Results of Ardila and Postnikov, Orlik and Terao,...

On Tutte polynomial uniqueness of twisted wheels

A graph G is called T -unique if any other graph having the same Tutte polynomial as G is isomorphic to G. Recently, there has been much interest in determining T -unique graphs and matroids. For example, de Mier and Noy [A. de Mier, M. Noy, On graphs determined by their Tutte polynomials, Graphs Combin. 20 (2004) 105–119; A. de Mier, M. Noy, Tutte uniqueness of line graphs, Discrete Math. 301 ...