## Bounds on connective constants of regular graphs    [PDF]

Geoffrey R. Grimmett, Zhongyang Li
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.
View original: http://arxiv.org/abs/1210.6277