One-matching bi-Cayley graphs over abelian groups

  • Authors:

  • István Kovács;Aleksander Malnič;Dragan Marušič;Štefko Miklavič

  • Affiliations:

  • University of Primorska, FAMNIT, Glagoljaska 8, 6000 Koper, Slovenia;University of Ljubljana, IMFM, Jadranska 19, 1111 Ljubljana, Slovenia;University of Primorska, FAMNIT, Glagoljaska 8, 6000 Koper, Slovenia and University of Ljubljana, IMFM, Jadranska 19, 1111 Ljubljana, Slovenia;University of Primorska, FAMNIT, Glagoljaska 8, 6000 Koper, Slovenia and University of Ljubljana, IMFM, Jadranska 19, 1111 Ljubljana, Slovenia

  • Venue:
  • European Journal of Combinatorics
  • Year:
  • 2009

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Abstract

A bi-Cayley graph is a graph which admits a semiregular group of automorphisms with two orbits (of equal size), and is a one-matching bi-Cayley graph if the bipartite graph induced by the edges joining these two orbits is a perfect matching. Typical examples of such graphs are the generalized Petersen graphs. A classification of connected arc-transitive one-matching bi-Cayley graphs over abelian groups is given. This is done without referring to the classification of finite simple groups. Instead, complex irreducible characters of abelian groups are used extensively.