For a graph G and a subgraph H of G, an H-decomposition of G is a partition of the edge set of G into subsets Ei,1⩽i⩽k, such that each Ei induces a graph isomorphic to H. A graph Γ(ℝ) is said to be non-zero zero divisor graph of commutative ring ℝ with identity if u,v∈V(Γ(ℝ)) and (u,v)∈E(Γ(ℝ)) if and only if uv=0. It is prove that complete decomposible into cycle of length 4 of an H-decomposition of the zero divisor graph Γ(ℝ) where H is any simple connected graph. In particular, we give a complete solution to the problem in the case Zp×Zp×Zp×,…,×Zp (n times). For any positive integer n>2, there exists a decomposition of Γ(ℝ) into cycle and stars in a commutative ring ℝ. We show that the obvious the graph Γ(ℝ) is decomposition into cycle and stars. Overall, the proposed of the graph Γ(ℝ) has significantly improved the decomposing to algebraic structure which can be useful for networking. In this paper we investigate the concept of Γ(ℝ) is decomposition into cycles and stars as a commutative rings R=Zp×Zp,Zp×Zp×Zp,Zp×Zp×Zp×Zp and Zp×Zp×Zp×,…,×Zp with p is a prime number. It is prove that the zero divisor graph Γ(R) is complete decomposible into cycle of length 4 and star. In particular, we give a complete solution to the problem in the case Zp×Zp×Zp×,…,×Zp (n times). For any positive integer n>2, there exists a decomposition of Γ(R) into cycle and stars in a commutative ring ℝ. We show that the obvious the graph Γ(R) is decomposition into cycle and stars. Overall, the proposed of the graph Γ(R) has significantly improved the decomposing to algebraic structure which can be useful for networking area.