The Tutte polynomial of the Sierpinski and Hanoi graphs

Abstract

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.

30 pages; title changed; revised exposition in the second version but results unchanged. arXiv admin note: substantial text overlap with arXiv:1010.2902

References in corpus (2)

• Counting dimer coverings on self-similar Schreier graphs
• The Tutte Polynomial of the Schreier graphs of the Grigorchuk group and the Basilica group

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• Connectedness and isomorphism properties of the zig-zag product of graphs
• Tutte polynomial of pseudofractal scale-free web
• Potts Partition Function Zeros and Ground State Entropy on Hanoi Graphs
• Horofunctions on Sierpiński type triangles
• Chromatic Zeros on the Limit $G_{\infty }^{(p,\ell )}$ of the Family $G_m^{(p,\ell )}$ of Hierarchical Graphs