Subspace graph topological space of graphs

A graph topology defined on a graph G is a collection ? of subgraphs of G which satisfies the properties such as K0, G ∈ ? and ? is closed under arbitrary union and finite intersection. Let (X, T) be a topological space and Y ⊆ X then, TY = {U ∩ Y : U ∈ T} is a topological space called a subspace topology or relative topology defined by T on Y. In this P1 we discusses the subspace or the relative graph topology defined by the graph topology ? on a subgraph H of G. We also study the properties of subspace graph topologies, open graphs, d-closed graphs and nbd-closed graphs of subspace graph topologies.