Finite 1-regular Cayley graphs of valency 5
type: Item
instance of: scholarly article
title: Finite 1-regular Cayley graphs of valency 5
zbMATH Open document ID: 1267.05140
DOI: 10.1155/2013/125916
author: Jing Jian Li
author: Xiao Jun Zhang
author: Ben Gong Lou
published in: International Journal of Combinatorics
publication date: 2013-06-10T00:00:00Z
review text: Summary: Let \(\Gamma = \operatorname{Cay}(G, S)\) and \(G \leq X \leq \operatorname{Aut}\Gamma\). We say \(\Gamma\) is \((X,1)\)-regular Cayley graph if \(X\) acts regularly on its arcs. \(\Gamma\) is said to be core-free if \(G\) is core-free in some \(X \leq \operatorname{Aut}(\operatorname{Cay}(G, S))\). In this paper, we prove that if an \((X, 1)\)-regular Cayley graph of valency 5 is not normal or binormal, then it is the normal cover of one of two core-free ones up to isomorphism. In particular, there are no core-free 1-regular Cayley graphs of valency 5.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 6172105
zbMATH Keywords: regular Cayley graph
zbMATH Keywords: normal cover
zbMATH Keywords: core-free Cayley graphs
Wikidata QID: Q58923538
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2013/125916
OpenAlex ID: W1986966550
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description: scientific article; zbMATH DE number 6172105