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The diameter of a random Cayley graph of Z_q

Gideon Amir·Ori Gurel-Gurevich
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Abstract

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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Gideon Amir, Ori Gurel-Gurevich. 2009-10-04. The diameter of a random Cayley graph of Z_q. https://arxiv.org/abs/math/0609620

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