One-matching bi-Cayley graphs over abelian groups
Dragan Marušič, Aleksander Malnič, István Kovács and Štefko Miklavčič
Eur. j. comb. Volume 30, Number 2, pp. 602-616, 2009. ISSN 0195-6698

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.

[Edit]