Abstract: This article explores the interface between topology and graph theory by associating a graph to each finite topological space and studying how topological properties are reflected in the corresponding graph. We prove that homeomorphic finite topological spaces yield isomorphic graphs. We also obtain a lower bound on the number of distinct non- topologies on an -point set.

Keywords: Topological graphs, Finite topological space, T_0 and T_1 spaces, Inequivalent topology, Distinct topology.
AMS Subject classification: 05C10

VOLUME 9 ISSUE 11 2025: 113-120