Bounds on connective constants of regular graphs

Published 23 Oct 2012 in math.CO, math-ph, math.MP, and math.PR | (1210.6277v2)

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.

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