Manuel Lladser, Primoz Potocnik, Jana Siagova, Jozef Siran and Mark C. Wilson, submitted to Random Structures and Algorithms, June 2006 (12 pages)
Abstract: We consider random Cayley digraphs of order with uniformly distributed generating set of size . Specifically, we are interested in the asymptotics of the probability such a Cayley digraph has diameter two as and . We find a sharp phase transition from 0 to 1 as the order of growth of increases past . In particular, if is asymptotically linear in , the probability converges exponentially fast to 1.