Partial difference triples
type: Item
instance of: scholarly article
title: Partial difference triples
zbMATH Open document ID: 0788.05094
DOI: 10.1023/A:1022475918250
author: Ka Hin Leung
author: Siu Lun Ma
published in: Journal of Algebraic Combinatorics
publication date: 1994-05-30T00:00:00Z
review text: A strongly regular graph \((V,E)\) on \(2n\) vertices is called a strongly regular semi-Cayley graph if it admits an automorphism group \(G\) of order \(n\) which has two orbits on \(V\). A graph as above w.r.t. a group \(G\) can be obtained by using three subsets \(C\), \(D\), \(D'\) in \(G\) satisfying suitable conditions which involve the parameters of the graph. A triple \((C,D,D')\) for which such conditions hold is called a partial difference triple. The authors determine all partial difference triples \((C,D,D')\) in a group \(G\) when \(\langle D \cup D' \rangle\) is contained in a proper normal subgroup of \(G\). Further, they examine the case when \(G\) is cyclic and add new examples to those already known in the literature. All possible parameters for partial difference triples w.r.t. a cyclic group are determined. Examples are given as well as applications to the study of regular Cayley graphs w.r.t. 2-groups admitting a cyclic subgroup of index 2.
Mathematics Subject Classification ID: 05E30
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05B10
zbMATH DE Number: 482249
zbMATH Keywords: difference set
zbMATH Keywords: strongly regular graph
zbMATH Keywords: semi-Cayley graph
zbMATH Keywords: automorphism group
zbMATH Keywords: partial difference triple
zbMATH Keywords: cyclic group
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 482249