The main topic of this paper is to describe the structure of some graph commutative - transitive finite rings. It is shown that every such ring is a direct sum of an indecomposable noncommutative ring of prime power order, and a commutative ring. If for each a, b, c ∈ R\Z(R) , ab = ba and bc = cb imply ac = ca , then the ring R is said to be commutativetransitive. In this paper, we present graph of commutative- transitive rings. We show that a ring R is commutative- transitive iff commutative graph R is a union of complete graphs and present property for which , the ring Mn(R) is not commutative-transitive.
