Strongly regular semi-Cayley graphs
type: Item
instance of: scholarly article
title: Strongly regular semi-Cayley graphs
zbMATH Open document ID: 0801.05070
DOI: 10.1023/A:1022476321014
author: M. J. de Resmini
author: Dieter Jungnickel
published in: Journal of Algebraic Combinatorics
publication date: 1993-03-15T00:00:00Z
review text: This paper studies strongly regular graphs \(G\) on \(2n\) vertices which admit a group of automorphisms \(\Gamma\) of order \(n\) with two orbits of length \(n\) on the vertices of \(G\), which are called semi-Cayley graphs. The Petersen and Hoffman-Singleton graphs provide examples. The authors use the group ring \(Z\Gamma\) to obtain non-existence results when \(\Gamma\) is Abelian. If \(G\) is the Cayley graph for a group which contains an Abelian subgroup \(\Gamma\) of index two then \(G\) is a semi-Cayley graph. This observation allows the authors to apply their theory to prove that the only strongly regular Cayley graphs for dihedral and generalised quaternion groups are the complete bipartite graphs \(K_{n,n}\). They conjecture that strongly regular Cayley graphs for groups with a cyclic normal subgroup of index two are trivial (i.e., complete bipartite). This conjecture is verified for 2-groups with order not equal to 16 or 64.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 130431
zbMATH Keywords: strongly regular graphs
zbMATH Keywords: semi-Cayley graphs
zbMATH Keywords: Cayley graph
MaRDI profile type: Publication
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full work available at URL: a:1022476321014
OpenAlex ID: W81150580
description: scientific article; zbMATH DE number 130431