The diameter of a random Cayley graph of Z_q

G. Amir; Ori Gurel-Gurevich

The diameter of a random Cayley graph of Z_q

G. Amir
, Ori Gurel-Gurevich

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	American English
Pages (from-to)	59-65
Journal	Groups – Complexity – Cryptology
Volume	2
Issue number	1
State	Published - 2006

Cite this

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title = "The diameter of a random Cayley graph of Z\_q",

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\textasciicircum{}(1/k). The same also holds when the generating set is taken to be a symmetric set of size 2k.",

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AB - 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.

UR - http://arxiv.org/abs/math/0609620

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JO - Groups – Complexity – Cryptology

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The diameter of a random Cayley graph of Z_q

Abstract

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