On the asymptotic enumeration of Cayley graphs

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dc.contributor.authorMorris, Joy
dc.contributor.authorMoscatiello, Mariapia
dc.contributor.authorSpiga, Pablo
dc.date.accessioned2025-12-13T20:41:35Z
dc.date.available2025-12-13T20:41:35Z
dc.date.issued2021
dc.descriptionOpen access article. Creative Commons Attribution 4.0 International license (CC BY 4.0) applies
dc.description.abstractIn this paper, we are interested in the asymptotic enumeration of Cayley graphs. It has previously been shown that almost every Cayley digraph has the smallest possible auto- morphism group: that is, it is a digraphical regular representation (DRR). In this paper, we approach the corresponding question for undirected Cayley graphs. The situation is com- plicated by the fact that there are two infinite families of groups that do not admit any graphical regular representation (GRR). The strategy for digraphs involved analysing sepa- rately the cases where the regular group R has a nontrivial proper normal subgroup N with the property that the automorphism group of the digraph fixes each N-coset setwise, and the cases where it does not. In this paper, we deal with undirected graphs in the case where the regular group has such a nontrivial proper normal subgroup.
dc.description.peer-reviewYes
dc.identifier.citationMorris, J., Moscatiello, M., & Spiga, P. (2021). On the asymptotic enumeration of Cayley graphs. Annali di Matematica pura e Applicata, 201(3), 1417-1461. https://doi.org/10.1007/s10231-021-01163-w
dc.identifier.urihttps://hdl.handle.net/10133/7257
dc.language.isoen
dc.publisherSpringer
dc.publisher.departmentDepartment of Mathematics and Computer Science
dc.publisher.facultyArts and Science
dc.publisher.institutionUniversity of Lethbridge
dc.publisher.institutionUniversity of Padova
dc.publisher.institutionUniversity of Milano-Bicocca
dc.publisher.urlhttps://doi.org/10.1007/s10231-021-01163-w
dc.subjectRegular representation
dc.subjectCayley graph
dc.subjectAutomorphism group
dc.subjectAsymptotic enumeration
dc.subjectGraphical regular representation
dc.subjectGRR
dc.subjectNormal Cayley graph
dc.subjectBabai-Godsil conjecture
dc.subjectXu conjecture
dc.titleOn the asymptotic enumeration of Cayley graphs
dc.typeArticle
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