Tutte polynomials of bracelets

Tutte Polynomials of Bracelets

The identity linking the Tutte polynomial with the Potts model on a graph implies the existence of a decomposition resembling that previously obtained for the chromatic polynomial. Specifically, let {Gn} be a family of bracelets in which the base graph has b vertices. Then the Tutte polynomial of Gn can be written as a sum of terms, one for each partition π of a non-negative integer ` ≤ b: (x− ...

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.

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,...