Enumeration of matchings in families of self-similar graphs

Authors:
Elmar Teufl;Stephan Wagner
Affiliations:
Fakultät für Mathematik, Universität Bielefeld, P.O.Box 100131, 33501 Bielefeld, Germany;Department of Mathematical Sciences, Stellenbosch University, Private Bag X1, Matieland 7602, South Africa
Venue:
Discrete Applied Mathematics
Year:
2010

Citing 4
Cited 2

The number of matchings in random regular graphs and bipartite graphs

Journal of Combinatorial Theory Series B
On acyclic systems with minimal Hosoya index

Discrete Applied Mathematics
Enumeration problems for classes of self-similar graphs

Journal of Combinatorial Theory Series A
An Asymptotic Independence Theorem for the Number of Matchings in Graphs

Graphs and Combinatorics

On the number of independent sets in cycle-separated tricyclic graphs

Computers & Mathematics with Applications
Counting dimer coverings on self-similar Schreier graphs

European Journal of Combinatorics

Quantified Score

Hi-index	0.04

Visualization

Abstract

The number of matchings of a graph G is an important graph parameter in various contexts, notably in statistical physics (dimer-monomer model). Following recent research on graph parameters of this type in connection with self-similar, fractal-like graphs, we study the asymptotic behavior of the number of matchings in families of self-similar graphs that are constructed by a very general replacement procedure. Under certain conditions on the geometry of the graphs, we are able to prove that the number of matchings generally follows a doubly exponential growth. The proof depends on an independence theorem for the number of matchings that has been used earlier to treat the special case of Sierpinski graphs. We also further extend the technique to the matching-generating polynomial (equivalent to the partition function for the dimer-monomer model) and provide a variety of examples.