随机Cayley图的直径

Groups Complex. Cryptol. Pub Date : 2010-06-01 DOI:10.1515/gcc.2010.004

Gideon Amir, O. Gurel-Gurevich

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引用次数: 12

摘要

考虑有k个一致选择生成元的素数阶q循环群的Cayley图。对于固定k，我们证明了所述图的直径是渐近的(在q中)阶的。这就回答了本杰明的一个问题。当发电集是一个大小为2k的对称集时，也是如此。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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 . 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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Groups Complex. Cryptol.

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