Bounds on connective constants of regular graphs

Geoffrey R. Grimmett, Zhongyang Li

Published 2012-10-23, updated 2013-05-01Version 2

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.