The diameter of a random Cayley graph of Z_q
Probability
2009-10-04 v2 Combinatorics
Metric Geometry
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.
Cite
@article{arxiv.math/0609620,
title = {The diameter of a random Cayley graph of Z_q},
author = {Gideon Amir and Ori Gurel-Gurevich},
journal= {arXiv preprint arXiv:math/0609620},
year = {2009}
}
Comments
8 pages