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The Tutte polynomial of the Sierpiński and Hanoi graphs
-
Alfredo Donno
and
Donatella Iacono
Published/Copyright:
October 1, 2013
Abstract
We study the Tutte polynomial of two infinite families of finite graphs: the Sierpi´nski graphs, which are finite approximations of the well-known Sierpi´nski 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.
Keywords: Tutte polynomial; Sierpi´nski graph; Schreier graph of the Hanoi Towers group; self-similar graph; spanning subgraph; acyclic orientation; reliability polynomial; chromatic polynomial; partition function of the Ising model
Published Online: 2013-10-01
Published in Print: 2013-10
© 2013 by Walter de Gruyter GmbH & Co.
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Articles in the same Issue
- Masthead
- Some remarks on Nijenhuis brackets, formality, and Kähler manifolds
- Semifields from skew polynomial rings
- A note on CR quaternionic maps
- On maximal curves of Fermat type
- On the singular locus of sets definable in a quasianalytic structure
- A product integral representation of mixed volumes of two convex bodies
- The Tutte polynomial of the Sierpiński and Hanoi graphs
- A lower bound for the Ricci curvature of submanifolds in generalized Sasakian space forms
- The canonical contact structure on the space of oriented null geodesics of pseudospheres and products
- Inscribable stacked polytopes
- Differential Harnack estimates for backward heat equations with potentials under an extended Ricci flow
