Almost all Cayley graphs have diameter 2 (Q1377827)

The main result is that the ratio of the number of (not necessarily connected) Cayley graphs of a group \(G\) having diameter 2 to the total number of Cayley graphs of \(G\) approaches 1 as \(|G|\) approaches infinity. Using a result of the reviewer [J. Comb. Theory 8, 23-29 (1970; Zbl 0185.51702)], the authors deduce that the edge-connectivity equals the valence in almost all Cayley graphs. There is a misprint at the end of the third paragraph. If \(G\) has order \(n\) while \(m\) of its elements have order 2, then it should read that there are exactly \(2^{(n+m-1)/2}\) Cayley graphs of \(G\).