https://hal.inria.fr/hal-00990591Lladser, Manuel E.Manuel E.LladserDepartment of Applied Mathematics [Boulder] - University of Colorado [Boulder]Potočnik, PrimožPrimožPotočnikFMF - Faculty of Mathematics and Physics [Ljubljana] - University of Ljubljana Širáň, JozefJozefŠiráňSchool of Mathematics and Statistics [Milton Keynes] - Faculty of Science, Technology, Engineering and Mathematics [Milton Keynes] - OU - The Open University [Milton Keynes]Department of Mathematics and Descriptive Geometry [Bratislava] - VSB - Technical University of Ostrava [Ostrava]Wilson, Mark C.Mark C.WilsonDepartment of Computer Science [Auckland] - University of Auckland [Auckland]Random Cayley digraphs of diameter 2 and given degreeHAL CCSD2012[INFO.INFO-DM] Computer Science [cs]/Discrete Mathematics [cs.DM]Inria Sophia Antipolis-Méditerranée / I3s, Service Ist2014-05-13 16:27:422020-10-15 12:00:042014-05-13 16:39:05enJournal articleshttps://hal.inria.fr/hal-00990591/document10.46298/dmtcs.588application/pdf1We 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.