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

Let GG be a finite group and AA a nonempty subset (possibly containing the identity element) of GG. The Bi-Cayley graph X=BC(G,A)X=BC(G,A) of GG with respect to AA is defined as the bipartite graph with vertex set G×{0,1}G×{0,1} and edge set {{(g,0),(sg,1)}∣g∈G,s∈A}{{(g,0),(sg,1)}∣g∈G,s∈A}. A graph ΓΓ admitting a perfect matching is called nn-extendable if ∣V(Γ)∣≥2n+2∣V(Γ)∣≥2n+2 and every matching of size nn in ΓΓ can be extended to a perfect matching of ΓΓ. In this paper, the extendability of Bi-Cayley graphs of finite abelian groups is explored. In particular, 22-extendable and 33-extendable Bi-Cayley graphs of finite abelian groups are characterized.