A NEW GRAPH TOPOLOGY ON DECOMPOSITION OF GRAPH

In this paper, we explore the extension of topological concepts to graph theory by defining a graph topology as a collection of sub-graphs within a graph G that satisfy properties analogous to the axioms of point-set topology. Specifically, we focus on the edge-induced sub-graph topology, where open sets are sub-graphs formed by subsets of the edge set E of G. Building upon this framework, we introduce the concept of an N -graph topological space, generated by these edge-induced sub-graphs. This novel approach facilitates a deeper exploration of the interplay between graph-theoretical structures and topological spaces, potentially leading to new insights and applications in both fields.