The diameter of a random Cayley graph of ℤq

Gideon Amir*, Ori Gurel-Gurevich

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

7 Scopus citations


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 languageAmerican English
Pages (from-to)59-65
Number of pages7
JournalGroups, Complexity, Cryptology
Issue number1
StatePublished - Jun 2010
Externally publishedYes


  • Random graphs
  • Random random walks


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