Pentavalent symmetric graphs of order \(2pq\)
type: Item
instance of: scholarly article
title: Pentavalent symmetric graphs of order \(2pq\)
zbMATH Open document ID: 1246.05072
author: Xiaohui Hua
author: Jaeun Lee
author: Yan-Quan Feng
published in: Discrete Mathematics
publication date: 2011-10-21T00:00:00Z
review text: In this paper, all connected pentavalent symmetric (1-arc-transitive) graphs of order \(2pq\) are classified, where \(p\) and \(q\) are distinct primes. It follows from the classification that there are two such graphs of order \(4p\) and, for odd primes \(p\) and \(q\), there is an infinite family of connected graphs of order \(2pq\) with solvable automorphism groups and there are seven sporadic ones with nonsolvable automorphism groups. The paper uses sophisticated group theoretic tools and the Sabidussi construction of 1-arc-transitive graphs as coset graphs Cos\((G,H,HaH)\) with \(H\leq G\), \(a^2\in H\) and \(\langle H, a \rangle = G\). The Magma computer algebra system is also used to determine when the coset graphs constructed are isomorphic.
reviewed by: Josef Lauri
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C85
zbMATH DE Number: 5961737
zbMATH Keywords: arc-transitive graph
zbMATH Keywords: pentavalent symmetric graph
zbMATH Keywords: \(s\)-regular graph
zbMATH Keywords: automorphism group
zbMATH Keywords: Sabidussi construction
zbMATH Keywords: coset graphs
zbMATH Keywords: Magma computer algebra system
describes a project that uses: Magma
MaRDI profile type: Publication
full work available at URL: j.disc.2011.07.007
OpenAlex ID: W2105654109
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DOI: 10.1016/J.DISC.2011.07.007
description: scientific article; zbMATH DE number 5961737