Topologized Bipartite Graph

Let G be bipartite graph with V vertices and E edges. A topological space X is a topologized graph if it satisfies the following conditions:

Every singleton is open or closed.

∀x∈X, ∣∂(x)∣≤2, where ∂(x) is a boundary of x.

Here the topology is defined on the graph, since the space X is the union of vertices and edges. This work is extended from topologized graph to star graph (0<n≤2), Bistar, Bipartite graph, Tree, complete bipartite graph.