Cubic vertex-transitive non-Cayley graphs of order \(8p\)
type: Item
instance of: scholarly article
title: Cubic vertex-transitive non-Cayley graphs of order \(8p\)
zbMATH Open document ID: 1243.05111
author: Jin-Xin Zhou
author: Yan-Quan Feng
published in: The Electronic Journal of Combinatorics
publication date: 2012-06-12T00:00:00Z
full work available at URL: v19i1p53
review text: Summary: A graph is vertex-transitive if its automorphism group acts transitively on its vertices. A vertex-transitive graph is a Cayley graph if its automorphism group contains a subgroup acting regularly on its vertices. In this paper, the cubic vertex-transitive non-Cayley graphs of order \(8p\) are classified for each prime \(p\). It follows from this classification that there are two sporadic and two infinite families of such graphs, of which the sporadic ones have order \(56\), one infinite family exists for every prime \(p>3\) and the other family exists if and only if \(p \equiv 1\mod 4\). For each family there is a unique graph for a given order.
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C60
Mathematics Subject Classification ID: 20B25
zbMATH DE Number: 6045677
zbMATH Keywords: Cayley graphs
zbMATH Keywords: vertex-transitive graphs
zbMATH Keywords: automorphism groups
describes a project that uses: Magma
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 6045677