In this paper we show that almost all Cayley digraphs have automorphism group as small as possible; that is, they are digraphical regular representations (DRRs). More precisely, we show that as r tends to infinity, for every finite group R of order r, out of all possible Cayley digraphs on R the proportion whose automorphism group is as small as possible tends to 1. This proves a natural conjecture first proposed in 1982 by Babai and Godsil.

中文翻译：

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Cayley有向图的渐近枚举

在本文中，我们证明了几乎所有的Cayley有向图都具有尽可能小的自同构群。也就是说，它们是字母正则表示法（DRR）。更确切地说，我们表明，随着r趋于无穷大，对于r阶的每个有限群R，在R上所有可能的Cayley有向图中，其同构群尽可能小的比例趋向于1。这证明了首先提出的自然猜想1982年由Babai和Godsil创作。