Construction A Topology On Graphs

Abstract

         In this paper, we have constructed a topology on graphs and a topology on subgraphs with examples. We proved that a graph is connected if, and only if, it is connected with respect to its topology.  Also, we gave given a new topological concept on two topologies and we called it symmetric with examples.

        Also, we proved that, if two graphs are isomorphic, then their topologies  are symmetric and we have shown by example that the converse  is not true in general.