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The Tutte polynomial of the Sierpiński and Hanoi graphs. (English) Zbl 1275.05030
Summary: We study the Tutte polynomial of two infinite families of finite graphs: the Sierpiński graphs, which are finite approximations of the well-known Sierpiński 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.

MSC:
05C31 Graph polynomials
05C15 Coloring of graphs and hypergraphs
05C30 Enumeration in graph theory
05C38 Paths and cycles
20E08 Groups acting on trees
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