Edge-symmetric distance-regular coverings of complete graphs: the almost simple case
type: Item
instance of: scholarly article
title: Edge-symmetric distance-regular coverings of complete graphs: the almost simple case
zbMATH Open document ID: 1434.05159
published in: Algebra and Logic
publication date: 2018-11-14T00:00:00Z
review text: Let \(\Gamma\) be a distance-regular covering of a complete graph. It is well-known that \(\Gamma\) is an antipodal graph of diameter~\(3\) and the antipodal classes of \(\Gamma\) are the blocks of the covering. Moreover, the intersection array of \(\Gamma\) can be written as \((k, (r-1)\mu, 1; 1, \mu, k)\), where \(r\) is the order of the antipodal class. The authors have been working on the classification of \(\Gamma\) when \(\Gamma\) is edge-transitive. In the preceding papers, they have finished it in the case of \(r\in\{2, k, (k-1)/\mu\}\). In this paper, they tackle the case \(r\notin\{2, k, (k-1)/\mu\}\) and give the classification under the assumption that the action of \(\operatorname{Aut}(G)\) on the set of the untipodal classes is almost simple.
reviewed by: Akira Saito
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C70
Mathematics Subject Classification ID: 05C12
zbMATH DE Number: 6979345
zbMATH Keywords: edge-symmetric graph
zbMATH Keywords: distance-regular graph
zbMATH Keywords: covering
zbMATH Keywords: antipodal class
zbMATH Keywords: complete graph
describes a project that uses: GAP
author: Alexandre A. Makhnev
author: Dmitriĭ Viktorovich Paduchikh
author: Ludmila Yur'evna Tsiovkina
MaRDI profile type: Publication
full work available at URL: s10469-018-9486-5
OpenAlex ID: W2883893916
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DOI: 10.1007/S10469-018-9486-5
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description: scientific article; zbMATH DE number 6979345