Strongly regular Cayley graphs over the group ℤp n⊕ℤpn

Yefim I. Leifman, Mikhail E. Muzychuk

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

Strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2 were studied in [J.A. Davis, Partial difference sets in p-groups, Arch. Math. 63 (1994) 103-110; K.H. Leung, S.L. Ma, Partial difference sets with Paley parameters, Bull. London Math. Soc. 27 (1995) 553-564]. It was shown that such graphs exist iff the corresponding group is isomorphic to Zpn⊕Zpn, where p is an odd prime. In this paper we classify all strongly regular Cayley graphs over this group using Schur ring method. As a consequence we obtain a complete classification of strongly regular Cayley graphs with Paley parameters over abelian groups of rank 2.

Original languageEnglish
Pages (from-to)219-239
Number of pages21
JournalDiscrete Mathematics
Volume305
Issue number1-3
DOIs
StatePublished - 6 Dec 2005
Externally publishedYes

Keywords

  • Cayley graph
  • Schur ring
  • Strongly regular graph

ASJC Scopus subject areas

  • Theoretical Computer Science
  • Discrete Mathematics and Combinatorics

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