Direct product and uniqueness of automorphism groups of graphs
type: Item
instance of: scholarly article
title: Direct product and uniqueness of automorphism groups of graphs
zbMATH Open document ID: 0943.05045
DOI: 10.1016/S0012-365X(99)00044-8
author: Wojciech Peisert
published in: Discrete Mathematics
publication date: 2000-09-05T00:00:00Z
review text: The author considers the problem of representing permutation groups by graphs. If \(\Aut(G)\) denotes the automorphism group of a graph \(G\) and \(A\equiv\Aut(G)\), then \(A\) is a representable permutation group. If \(A\) is represented by exactly one graph \(G\) (up to isomorphism), then \(A\) is called unique. The main result is the following theorem: Let \(A_1\) and \(A_2\) be representable permutation groups. Then the direct product \(A_1\otimes A_2\) is not representable iff \(A_1\) and \(A_2\) are transitive, unique and isomorphic as permutation groups. Moreover all unique transitive permutation groups of prime degree are described.
Mathematics Subject Classification ID: 05C25
zbMATH DE Number: 1382641
zbMATH Keywords: automorphism group
zbMATH Keywords: representable permutation group
reviewed by: Ulrike Baumann
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1382641