On The Extendability Of Semi-Cayley Graph And It's Applications

A semi-Cayley graph is a graph which admits a semiregular automorphism group with two orbits of equal size.A connected graphΓwith at least 2n+2 vertices is said to be n-extendable if every matching of size n inΓcan be extended to a perfect matching.The aim of this paper is to study the 1-extendable and 2-extendable semi-Cayley graphs SC(G;A,B,C) over finite abelian groups with the additional condition that A=B.As applications, the 2-extendable Cayley graphs over dihedral groups and generalized dicyclic groups are classified,respectively.We also prove that semi-Cayley graphs over finite abelian groups contains Cayley graphs over finite abelian groups with even order.