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arXiv · 1811.07709

Asymptotic enumeration of Cayley digraphs

Joy Morris·Pablo Spiga
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Abstract

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.

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Joy Morris, Pablo Spiga. 2018-11-19. Asymptotic enumeration of Cayley digraphs. https://arxiv.org/abs/1811.07709

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