The Tutte polynomial of the Sierpinski and Hanoi graphs

TL;DR

This paper derives recursive formulas for the Tutte polynomial of Sierpinski and Hanoi graphs, providing insights into their combinatorial properties and special evaluations.

Contribution

It introduces recursive descriptions of the Tutte polynomial for these graph families, a novel approach for analyzing their combinatorial structure.

Findings

Recursive formulas for the Tutte polynomial of Sierpinski graphs

Recursive formulas for the Tutte polynomial of Hanoi graphs

Computed special evaluations revealing combinatorial insights

Abstract

We study the Tutte polynomial of two infinite families of finite graphs: the Sierpi\'{n}ski graphs, which are finite approximations of the well-known Sierpi\'{n}ski gasket, and the Schreier graphs of the Hanoi Towers group $H^{(3)}$ acting on the rooted ternary tree. For both of them, we recursively describe the Tutte polynomial and we compute several special evaluations of it, giving interesting results about the combinatorial structure of these graphs.