On classification of extendability of cayley graphs on dicyclic groups

Abstract

Let G be a group and S a subset of G such that the identity element 1 ∉ S and x_-l ε S for each x ε S. The Cayley graph X(G;S) on a group G has the elements of G as its vertices and edges joining g and gs for all g ε G and s ε S. A graph is said to be Κ-extendable if it contains k independent edges and any k independent edges can be extended to a perfect matching. In this paper, we prove that every connected Cayley graph on dicyclic groups is 2-extendable and also investigate the 3-extendability in X(G;S).