Abstract

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.

Keywords and Phrases

Graph Topology, Edge-Induced sub graph Topology, N -Graph Topological Space, N-Graph Topology, N-open sub graph, N-closed sub graph, N-graph Interior, N-graph closure.

A.M.S. subject classification

05C62, 05C75, 54A05.

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