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.