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The diameter of a random Cayley graph of ℤq
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Gideon Amir
Published/Copyright:
June 23, 2010
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 2k.
Keywords.: Random random walks; random graphs
Received: 2009-07-29
Published Online: 2010-06-23
Published in Print: 2010-June
© de Gruyter 2010
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- Presentations of matrix rings
- The diameter of a random Cayley graph of ℤq
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Articles in the same Issue
- On Shephard groups with large triangles
- An update on Hurwitz groups
- Presentations of matrix rings
- The diameter of a random Cayley graph of ℤq
- Challenge response password security using combinatorial group theory
- The discrete logarithm problem in the group of non-singular circulant matrices
- Algebraic geometry over natural numbers. The classification of coordinate monoids
