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The diameter of a random Cayley graph of ℤ q

The diameter of a random Cayley graph of ℤ q 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 . http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Groups - Complexity - Cryptology de Gruyter

The diameter of a random Cayley graph of ℤ q

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Publisher
de Gruyter
Copyright
© de Gruyter 2010
ISSN
1867-1144
eISSN
1869-6104
DOI
10.1515/GCC.2010.004
Publisher site
See Article on Publisher Site

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 . 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 .

Journal

Groups - Complexity - Cryptology – de Gruyter

Published: Jun 1, 2010

Keywords: Random random walks; random graphs

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