On the extendability of certain semi-Cayley graphs of finite abelian groups

A connected graph Γ with at least 2n+2 vertices is said to be n-extendable if every matching of size n in Γ can be extended to a perfect matching. The aim of this paper is to study the 1-extendability and 2-extendability of certain semi-Cayley graphs of finite abelian groups, and the classification of connected 2-extendable semi-Cayley graphs of finite abelian groups is given. Thus the 1-extendability and 2-extendability of Cayley graphs of non-abelian groups which can be realized as such semi-Cayley graphs of abelian groups can be deduced. In particular, the 1-extendability and 2-extendability of connected Cayley graphs of generalized dicyclic groups and generalized dihedral groups are characterized.