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Annals of Combinatorics

, 15:355 | Cite as

The Number of Spanning Trees in Self-Similar Graphs

  • Elmar TeuflEmail author
  • Stephan Wagner
Article

Abstract

The number of spanning trees of a graph, also known as the complexity, is computed for graphs constructed by a replacement procedure yielding a self-similar structure. It is shown that under certain symmetry conditions exact formulas for the complexity can be given. These formulas indicate interesting connections to the theory of electrical networks. Examples include the well-known Sierpiński graphs and their higher-dimensional analogues. Several auxiliary results are provided on the way—for instance, a property of the number of rooted spanning forests is proven for graphs with a high degree of symmetry.

Mathematics Subject Classification

05C30 05C05 34B45 

Keywords

spanning trees self-similar graphs 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Fachbereich MathematikEberhard Karls Universität TübingenTübingenGermany
  2. 2.Department of Mathematical SciencesStellenbosch UniversityMatielandSouth Africa

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