On the extendability of Bi-Cayley graphs of finite abelian groups

Let G be a finite group and A a nonempty subset (possibly containing the identity element) of G. The Bi-Cayley graph X = BC(G. A) of G with respect to A is defined as the bipartite graph with vertex set G x {0, 1} and edge set {{(g, 0), (sg, 1)} | g epsilon G. S epsilon A). A graph Gamma admitting a perfect matching is called n-extendable if | V(Gamma) | >= 2n + 2 and every matching of size n in Gamma can be extended to a perfect matching of Gamma. In this paper, the extendability of Bi-Cayley graphs of finite abelian groups is explored. In particular, 2-extendable and 3-extendable Bi-Cayley graphs of finite abelian groups are characterized. (C) 2009 Elsevier B.V. All rights reserved.