The number of spanning trees in self-similar graphs

DOI10.1007/s00026-011-0100-yzbMath1234.05123OpenAlexW2115821419MaRDI QIDQ659629

Elmar Teufl, Stephan G. Wagner

Publication date: 24 January 2012

Published in: Annals of Combinatorics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00026-011-0100-y

zbMATH Keywords

spanning treesself-similar graphs

Mathematics Subject Classification ID

Trees (05C05) Enumeration in graph theory (05C30) Boundary value problems on graphs and networks for ordinary differential equations (34B45)

Related Items (12)

Regularized Laplacian determinants of self-similar fractals ⋮ A general method for computing Tutte polynomials of self-similar graphs ⋮ Entropy and enumeration of spanning connected unicyclic subgraphs in self-similar network ⋮ Abelian sandpiles on Sierpiński gasket graphs ⋮ The number and degree distribution of spanning trees in the Tower of Hanoi graph ⋮ Resistance scaling and the number of spanning trees in self-similar lattices ⋮ COUNTING SPANNING TREES IN PRISM AND ANTI-PRISM GRAPHS ⋮ Spectral decimation of the magnetic Laplacian on the Sierpinski gasket: solving the Hofstadter-Sierpinski butterfly ⋮ Potts model partition functions on two families of fractal lattices ⋮ Correct proof of the main result in ``The number of spanning trees of a class of self-similar fractal models by Ma and Yao ⋮ Determinant identities for Laplace matrices ⋮ Exact and asymptotic enumeration of perfect matchings in self-similar graphs

Cites Work

• Spanning trees on the Sierpinski gasket
• Some determinant expansions and the matrix-tree theorem
• The short-cut test
• Some methods for counting the spanning trees in labelled molecular graphs, examined in relation to certain fullerenes
• On eigenvalue problems for Laplacians on p.c.f. self-similar sets
• Enumeration problems for classes of self-similar graphs
• Random walks on infinite self-similar graphs
• A trace on fractal graphs and the Ihara zeta function
• A Combinatorial Proof of the All Minors Matrix Tree Theorem
• Spectral properties of self-similar lattices and iteration of rational maps
• Growth of Self‐Similar Graphs
• Spanning trees on graphs and lattices inddimensions
• Asymptotic Enumeration of Spanning Trees
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