The Tutte polynomial of some self-similar graphs

Details The Tutte polynomial of some self-similar graphs The Tutte polynomial of some self-similar graphs

2010-06-28

arxiv.org/abs/1006.5333v1

Mathematics

Combinatorics

30 pages

Scientific paper

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.

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