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The diameter of a random Cayley graph of Zq

By Gideon Amir and Ori Gurel-gurevich


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 k √ q. This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.

Year: 2009
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