Bounds on connective constants of regular graphs
Combinatorics
2013-05-02 v2 Mathematical Physics
math.MP
Probability
Abstract
Bounds are proved for the connective constant \mu\ of an infinite, connected, \Delta-regular graph G. The main result is that \mu\ \ge \sqrt{\Delta-1} if G is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.
Keywords
Cite
@article{arxiv.1210.6277,
title = {Bounds on connective constants of regular graphs},
author = {Geoffrey R. Grimmett and Zhongyang Li},
journal= {arXiv preprint arXiv:1210.6277},
year = {2013}
}
Comments
v2: small fix applied to Thm 3.2