Counting self-avoiding walks on free products of graphs

Lorenz A. Gilch; Sebastian Müller

doi:10.1016/j.disc.2016.08.018

Counting self-avoiding walks on free products of graphs

Lorenz A. Gilch^*, Sebastian Müller

^*Korrespondierende/r Autor/-in für diese Arbeit

Institut für Diskrete Mathematik (5050)

Publikation: Beitrag in einer Fachzeitschrift › Artikel › Begutachtung

Abstract

The connective constantμ(G) of a graph G is the asymptotic growth rate of the number σ_n 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 σ_n∼A_Gμ(G)ⁿ for some constant A_G 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.

Originalsprache	englisch
Seiten (von - bis)	325-332
Seitenumfang	8
Fachzeitschrift	Discrete Mathematics
Jahrgang	340
Ausgabenummer	3
DOIs	https://doi.org/10.1016/j.disc.2016.08.018
Publikationsstatus	Veröffentlicht - 1 März 2017

ASJC Scopus subject areas

Theoretische Informatik
Diskrete Mathematik und Kombinatorik

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10.1016/j.disc.2016.08.018

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Counting self-avoiding walks on free products of graphs

Abstract

ASJC Scopus subject areas

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