Some properties of unitary addition Cayley graphs

Let Γ be an abelian group and B be a subset of Γ. The addition Cayley graph G′ = Cay(Γ, B) is the graph having the vertex set V (G′) = Γ and the edge set E(G′) = {ab : a + b ∈ B}, where a, b ∈ Γ. 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 set of all units of the ring Zn, then two vertices a, b are adjacent if and only if a + b ∈ Un. The unitary addition Cayley graph Gn is also defined as, Gn = Cay(Zn, Un). In this paper, we discuss the several properties of unitary addition Cayley graphs and also obtain the characterization of planarity and outerplanarity of unitary addition Cayley graphs.