Regular sets in Cayley sum graphs on generalized dicyclic groups

For a graph Γ= (V (Γ), E (Γ) ), a subset C of V (Γ) is called an (α, β) -regular set in Γ, if every vertex of C is adjacent to exactly α vertices of C and every vertex of V (Γ) C is adjacent to exactly β vertices of C. In particular, if C is an (α, β) -regular set in some Cayley sum graph of a finite group G with connection set S, then C is called an (α, β) -regular set of G. In this paper, we consider a generalized dicyclic group G and for each subgroup H of G, by giving an appropriate connection set S, we determine each possibility for (α, β) such that H is an (α, β) -regular set of G.