Enumeration problems for classes of self-similar graphs

DOI10.1016/j.jcta.2007.01.007zbMath1124.05046OpenAlexW2153120082MaRDI QIDQ2384571

Elmar Teufl, Stephan G. Wagner

Publication date: 10 October 2007

Published in: Journal of Combinatorial Theory. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcta.2007.01.007

zbMATH Keywords

enumerationpolynomial recursionSelf-similar graph

Mathematics Subject Classification ID

Enumeration in graph theory (05C30) Graphs and linear algebra (matrices, eigenvalues, etc.) (05C50) Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) (05C70)

Related Items (11)

Copy-paste trees and their growth rates ⋮ Maximum matchings and minimum dominating sets in Apollonian networks and extended tower of Hanoi graphs ⋮ Enumeration of matchings in families of self-similar graphs ⋮ The number and degree distribution of spanning trees in the Tower of Hanoi graph ⋮ The Tutte polynomial of a class of compound graphs and its applications ⋮ Resistance scaling and the number of spanning trees in self-similar lattices ⋮ Using edge generating function to solve monomer-dimer problem ⋮ The number of spanning trees in self-similar graphs ⋮ Correct proof of the main result in ``The number of spanning trees of a class of self-similar fractal models by Ma and Yao ⋮ An asymptotic independence theorem for the number of matchings in graphs ⋮ Exact and asymptotic enumeration of perfect matchings in self-similar graphs

Uses Software

• OEIS

Cites Work

• Counting matchings in graphs
• Twelve countings with rooted plane trees
• Random walk statistics on fractal structures
• The number of matchings in random regular graphs and bipartite graphs
• Random walks on trees with finitely many cone types
• On subtrees of trees
• Fractals in Graz 2001. Analysis, dynamics, geometry, stochastics. Proceedings of the conference, Graz, Austria, June 2001
• Green functions on self-similar graphs and bounds for the spectrum of the Laplacian
• Pure point spectrum of the Laplacians on fractal graphs
• On maximal independent sets of nodes in trees
• Listing and Counting Subtrees of a Tree
• The Number of Independent Sets in a Grid Graph
• Spectral properties of self-similar lattices and iteration of rational maps
• Asymptotics of the transition probabilities of the simple random walk on self-similar graphs
• Growth of Self‐Similar Graphs
• Random Walks on Infinite Graphs and Groups
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