The diameter of a random Cayley graph of ℤq

Gideon Amir; Ori Gurel-Gurevich

doi:10.1515/gcc.2010.004

The diameter of a random Cayley graph of ℤ_q

Gideon Amir
, Ori Gurel-Gurevich

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

7 Scopus citations

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 k√q. This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.

Original language	English
Pages (from-to)	59-65
Number of pages	7
Journal	Groups, Complexity, Cryptology
Volume	2
Issue number	1
DOIs	https://doi.org/10.1515/gcc.2010.004
State	Published - Jun 2010
Externally published	Yes

Keywords

Random graphs
Random random walks

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10.1515/gcc.2010.004

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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 k√q. This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.",

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author = "Gideon Amir and Ori Gurel-Gurevich",

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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 k√q. This answers a question of Benjamini. The same also holds when the generating set is taken to be a symmetric set of size 2k.

KW - Random graphs

KW - Random random walks

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The diameter of a random Cayley graph of ℤ_q

Abstract

Keywords

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