Automorphism groups of primitive distance-bitransitive graphs are almost simple
type: Item
instance of: scholarly article
title: Automorphism groups of primitive distance-bitransitive graphs are almost simple
zbMATH Open document ID: 0632.05033
DOI: 10.1016/S0195-6698(87)80010-0
author: John Shawe-Taylor
published in: European Journal of Combinatorics
publication date: 1987-01-01T00:00:00Z
review text: Let \(\{\) A,B\(\}\) be a bipartition of a connected, nonisovalent, noncomplete bipartite graph \(\Gamma\). Let \(G\leq aut(\Gamma)\) satisfy the condition: given \(a_ 1,a_ 2\in A\) and \(b_ 1,b_ 2\in B\), with \(d(a_ 1,b_ 1)=d(a_ 2,b_ 2)\), there exists \(\phi\in G\) such that \(\phi (a_ 1)=a_ 2\) and \(\phi (b_ 1)=b_ 2\). Then (G,\(\Gamma)\) is called a distance-bitransitive pair. The main result is that, if (G,\(\Gamma)\) is such a pair, then G is almost simple, i.e., there exists a finite nonabelian simple group T such that \(T\leq G\leq aut(T)\). The proof is heavily dependent upon a theorem of \textit{C. Praeger, J. Saxl} and \textit{K. Yokoyama} [Proc. Lond. Math. Soc., III. Ser. 55, 1-21 (1987; Zbl 0619.05026)], one of the cases (concerning Hamming graphs) of which is pursued to some depth.
reviewed by: Mark E. Watkins
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05B20
Mathematics Subject Classification ID: 20B25
Mathematics Subject Classification ID: 20D06
zbMATH DE Number: 4027504
zbMATH Keywords: distance-transitive
zbMATH Keywords: primitive
zbMATH Keywords: imprimitive
zbMATH Keywords: distance-bitransitive pair
zbMATH Keywords: almost simple
zbMATH Keywords: Hamming graphs
MaRDI profile type: Publication
cites work: Antipodal covering graphs
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cites work: PRIMITIVE AND IMPRIMITIVE GRAPHS
full work available at URL: s0195-6698(87)80010-0
OpenAlex ID: W2069277447
description: scientific article; zbMATH DE number 4027504