%0 Journal Article
%T Counting self-avoiding walks on free products of graphs
%+ Institut für Mathematische Strukturtheorie (Math C) (TU Graz)
%+ Institut de Mathématiques de Marseille (I2M)
%A Gilch, Lorenz A.
%A Müller, Sebastian
%Z The research was supported by the exchange programme Amadeus-Amadée 31473TF.
%Z 10 pages
%< avec comité de lecture
%@ 0012-365X
%J Discrete Mathematics
%I Elsevier
%V 340
%N 3
%P 325 - 332
%8 2017-03
%D 2017
%Z 1509.03209
%R 10.1016/j.disc.2016.08.018
%K connective constant
%K self-avoiding walk
%K free product of graphs
%Z 05C30 (20E06 60K35)
%Z Mathematics [math]/Probability [math.PR]Journal articles
%X The connective constant $\mu(G)$ of a graph $G$ is the asymptotic growth rate of the number $\sigma_{n}$ 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 $\sigma_{n}\sim A_{G} \mu(G)^{n}$ for some constant $A_{G}$ that depends on $G$. In the case of finite products $\mu(G)$ can be calculated explicitly and is shown to be an algebraic number.
%G English
%L hal-01285401
%U https://hal.science/hal-01285401
%~ CNRS
%~ UNIV-AMU
%~ EC-MARSEILLE
%~ I2M
%~ I2M-2014-