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# Bounds on connective constants of regular graphs

(23 Oct 2012)  Key: citeulike:11534332

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### Abstract

Bounds are proved for the connective constant $μ$ of an infinite, connected, $Δ$-regular graph $G$. The main result is that $μ ≥ \sqrtΔ-1$ if $G$ is vertex-transitive and simple. This inequality is proved subject to weaker conditions under which it is sharp.