# Geodetic Decomposition of Zero Divisor Graph

## Main Article Content

## Abstract

A graph is said to be non-zero zero divisor graph of commutative ring with identity if and if and only if . Let denote a balanced complete bipartite graph with parts of size n and let denote a star with k edges. Let denotes a cycle of length K, i.e., . Let be the decomposition of complete bipartite graph. Let be a family of subgraphs of . An L-decomposition of G is an edge-disjoint decomposition of into positive integer copies of where . Furthermore, if each is isomorphic to a graph H, then we say that G has an H-decomposition. In this paper, we investigate the concept of geodetic decomposition of zero divisor graph. Let be the zero divisor graph. For a non-empty set of we define , for some , where is the closed interval consisting of and all vertices lying on some geodesic of . We have discussed the geodetic number of zero divisor graph and determine the geodesic decomposition of zero divisor graph of the ring .