The Tutte polynomial of the Sierpinski and Hanoi graphs

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.