Restrained Domination in Topologized Fuzzy Graph

Let  be a simple fuzzy graph. A subset of is said to be a restrained dominating set if every vertex in is adjacent to atleast one vertex in   as well as adjacent to another vertex in   A topologized graph  is a topological space such that every singleton is open or closed and for all  Since  is denoted by the boundary of a point x. In this paper defined an upper bound of restrained domination in topologized graph and restrained domination in topologized fuzzy graph. The discussion extends to analyse basic properties of topologized restrained dominating number, topologized restrained dominating set, topologized restrained dominating set in fuzzy graph.