Partial difference triples
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.
scientific article; zbMATH DE number 482249
scientific article