Double Domination Number In The Unitary Addition Cayley Graphs

Let (Γ,*) be a finite group and e be its identity. Let A be a generating set of Γ such that e A and a -1 ∈ A for all a ∈ A. The Cayley graph is defined by G = (V(G), E(G)), where V(G) = Γ and E(G)={(x, x*a)│x ∈ V(G), a ∈ A}, denoted by Cay(Γ,A). For a positive integer n > 1, the unitary addition Cayley graph Gn is the graph whose vertex set is Zn, the integers modulo n and if Un denotes the set of all units of the ring Zn, then two vertices a, b are adjacent if and only if a + b ∈ Un. In this paper, we attempt to find the double domination number of the unitary addition Cayley graphs Gn for some n.