Strongly regular Cayley graphs over primary abelian groups of rank 2

Yefim I. Leifman, Mikhail E. Muzychuk

Research output: Working paper/PreprintPreprint

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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 ${\mathbb Z}_{p^n} \oplus {\mathbb Z}_{p^n}$, where $p$ is an odd prime. In this paper we classify all strongly regular Cayley graphs over this group using Schur rings 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 GB
PublisherarXiv:math/0603518 [math.CO]
StatePublished - 2006

Keywords

  • math.CO

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