Symmetric graphs of order a product of two distinct primes
type: Item
instance of: scholarly article
title: Symmetric graphs of order a product of two distinct primes
zbMATH Open document ID: 0793.05071
author: Cheryl E. Praeger
author: Mingyao Xu
author: Ruji Wang
published in: Journal of Combinatorial Theory. Series B
publication date: 1994-08-15T00:00:00Z
review text: A simple undirected graph \(\Gamma\) is said to be symmetric if its automorphism group \(\Aut\Gamma\) is transitive on the set of ordered pairs of adjacent vertices of \(\Gamma\), and \(\Gamma\) is said to be imprimitive if \(\Aut\Gamma\) acts imprimitively on the vertices of \(\Gamma\). Let \(k\) and \(p\) be distinct primes with \(k< p\). This paper gives a classification of all imprimitive symmetric graphs on \(kp\) vertices for \(k\geq 5\). The cases \(k<5\) have been treated previously by Cheng and Oxley \((k=2)\) and the second and third authors \((k=3)\) (see item Zbl 0793.05074 below), and the classification of primitive symmetric graphs on \(kp\) vertices with \(k\geq 5\) was done by the first and third authors (see the following item Zbl 0793.05072).
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 572452
zbMATH Keywords: automorphism group
zbMATH Keywords: imprimitive symmetric graphs
zbMATH Keywords: primitive symmetric graphs
MaRDI profile type: Publication
full work available at URL: jctb.1993.1046
OpenAlex ID: W1980392696
Wikidata QID: Q56988345
DOI: 10.1006/JCTB.1993.1046
description: scientific article; zbMATH DE number 572452