The diameter of a random Cayley graph of ℤ q
Amir, Gideon; Gurel-Gurevich, Ori
2010-06-01 00:00:00
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 . This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2 k .
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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 . This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2 k .
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