Discrete Mathematics & Theoretical Computer Science 
We consider random Cayley digraphs of order n with uniformly distributed generating sets of size k. Specifically, we are interested in the asymptotics of the probability that such a Cayley digraph has diameter two as n > infinity and k = f(n), focusing on the functions f(n) = left perpendicularn(delta)right perpendicular and f(n) = left perpendicularcnright perpendicular. In both instances we show that this probability converges to 1 as n > infinity for arbitrary fixed delta is an element of (1/2, 1) and c is an element of (0, 1/2), respectively, with a much larger convergence rate in the second case and with sharper results for Abelian groups.
Source : ScholeXplorer
IsRelatedTo ARXIV 1202.6673 Source : ScholeXplorer IsRelatedTo DOI 10.1016/j.ejc.2013.06.030 Source : ScholeXplorer IsRelatedTo DOI 10.48550/arxiv.1202.6673
