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The diameter of random Cayley digraphs of given degree
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 at around . In particular, if is asymptotically linear in , the
probability converges exponentially fast to 1.Comment: 11 page