• CYCLIC PATH COVERS IN ZERO DIVISOR GRAPH

Abstract

Let R be a commutative ring and let  be the zero divisor graph of a commutative ring R, whose vertices are non- zero zero divisors of  , and such that the two vertices u,v are adjacent if n divides uv. In this paper, we have analyzed the maximum number of zero divisor graph , where  is a positive integer, by studying its properties and structure and thereby decomposing it into  a finite number of paths and cycles, whose sum of the vertices in the cycle are equal where decomposition is a set of subgraphs H₁,…H_k that partition of the edges of G. That is for all i and j is and