Geodesic
Almost all Cayley maps are mapical regular representations
Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article no. 01, 9 p.

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Cayley maps are combinatorial structures built upon Cayley graphs on a group. As such the original group embeds in their group of automorphisms, and one can ask in which situation the two coincide (one then calls the Cayley map  a mapical regular representation or MRR) and with what probability. The first question was answered by Jajcay. In this paper we tackle the probabilistic version, and prove that as groups get larger the proportion of MRRs among all Cayley Maps approaches 1.
DOI : 10.26493/1855-3974.3071.37e
Keywords: Regular representation, Cayley map, automorphism group, asymptotic enumeration, graphical regular representation, GRR 
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Pablo Spiga; Dario Sterzi. Almost all Cayley maps are mapical regular representations. Ars Mathematica Contemporanea, Tome 24 (2024) no. 1, article  no. 01, 9 p. doi : 10.26493/1855-3974.3071.37e. http://geodesic.mathdoc.fr/articles/10.26493/1855-3974.3071.37e/

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