Let Γ(V, E) be a graph. The Cayley graph of group (G,∗) and a subset S is a graph denoted by C
a
y(G, S), it is with vertex set V(C
a
y(G, S)) = G and two vertices x, y ∈ G are join if and only if y = x
s ∈ 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 C
n
and Dihedral Group D
2n
.