arXiv:1210.6277·math.CO·May 2, 2013·Comb.·2 cites
Bounds on connective constants of regular graphs
Geoffrey R. Grimmett, Zhongyang Li
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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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Taxonomy
TopicsGraph theory and applications · Advanced Graph Theory Research · Limits and Structures in Graph Theory