Counting self-avoiding walks on free products of graphs

Lorenz A. Gilch, Sebastian Müller

Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

Abstract

The connective constantμ(G) of a graph G is the asymptotic growth rate of the number σn of self-avoiding walks of length n in G from a given vertex. We prove a formula for the connective constant for free products of quasi-transitive graphs and show that σn∼AGμ(G)n for some constant AG that depends on G. In the case of products of finite graphs μ(G) can be calculated explicitly and is shown to be an algebraic number.

Originalspracheenglisch
Seiten (von - bis)325-332
Seitenumfang8
FachzeitschriftDiscrete Mathematics
Jahrgang340
Ausgabenummer3
DOIs
PublikationsstatusVeröffentlicht - 1 Mär 2017

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Free Product
Self-avoiding Walk
Counting
Graph in graph theory
Algebraic number
Finite Graph
Vertex of a graph

Schlagwörter

    ASJC Scopus subject areas

    • !!Theoretical Computer Science
    • !!Discrete Mathematics and Combinatorics

    Dies zitieren

    Counting self-avoiding walks on free products of graphs. / Gilch, Lorenz A.; Müller, Sebastian.

    in: Discrete Mathematics, Jahrgang 340, Nr. 3, 01.03.2017, S. 325-332.

    Publikation: Beitrag in einer FachzeitschriftArtikelForschungBegutachtung

    Gilch, Lorenz A. ; Müller, Sebastian. / Counting self-avoiding walks on free products of graphs. in: Discrete Mathematics. 2017 ; Jahrgang 340, Nr. 3. S. 325-332.
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