The Tutte Polynomial of the Schreier graphs of the Grigorchuk group and the Basilica group

Details The Tutte Polynomial of the Schreier graphs of the Grigorchuk group and the Basilica group The Tutte Polynomial of the Schreier graphs of the Grigorchuk group and the Basilica group

2010-10-14

arxiv.org/abs/1010.2902v1

Mathematics

Combinatorics

18 pages

Scientific paper

We study the Tutte polynomial of two infinite families of finite graphs. These are the Schreier graphs associated with the action of two well-known self-similar groups acting on the binary rooted tree by automorphisms: the first Grigorchuk group of intermediate growth, and the iterated monodromy group of the complex polynomial $z^2-1$ known as the Basilica group. For both of them, we describe the Tutte polynomial and we compute several special evaluations of it, giving further information about the combinatorial structure of these graphs.

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