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 = B C ( G , A ) of G with respect to A is defined as the bipartite graph with vertex set G × { 0 , 1 } and edge set { { ( g , 0 ) , ( s g , 1 ) } ∣ g ∈ G , s ∈ A } . A graph Γ admitting a perfect matching is called n -extendable if ∣ V ( Γ ) ∣ ≥ 2 n + 2 and every matching of size n in Γ can be extended to a perfect matching of Γ . 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.