The diameter of a random Cayley graph of Z_q
classification
🧮 math.PR
math.COmath.MG
keywords
graphcayleydiameterorderasymptoticallychosenconsidercyclic
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Consider the Cayley graph of the cyclic group of prime order q with k uniformly chosen generators. For fixed k, we prove that the diameter of said graph is asymptotically (in q) of order q^(1/k). The same also holds when the generating set is taken to be a symmetric set of size 2k.
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