The diameter of a random Cayley graph of Z_q

Details The diameter of a random Cayley graph of Z_q The diameter of a random Cayley graph of Z_q

2006-09-21

arxiv.org/abs/math/0609620v2

Mathematics

Probability

8 pages

Scientific paper

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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