worood mohammedsalah mahdi alkhalide

Abstract. Let Γ(V,E) be a graph. The Cayley graph of group (G,*) and a subset S is a graph denoted by Cay(G,S), it is with vertex set V (Cay(G,S)) = G and two vertices x,y ∈ G are join if and only if y = xs ∈ S for some s ∈ S. In this paper, we obtain characteristics of Cayley graphs under some graph operations, Graph direct product, Graph tenser product, Graph strong product when G isomorphic to Cyclic group Cn and Dihedral Group D2n

Let Γ(V, E) be a simple graph. The vertices set of graph is define {v1, v2, . . . , vn}. The common neighborhood graph (congraph) of graph Γ(V, E) is denoted by con(Γ(V, E)) such that any two vertices vi and vj are adjacent if and only they have N (vi) ∩ N (vj) ∅. The neighborhood of a vertex v is the set of all vertices u such that they are the endpoints of the same edge and denoted by N (v).

The cyclic graph of finite graph