STRUCTURAL PROPERTIES OF TOPOLOGICAL GRAPHS
Manohar S. H.1,2, Vijendra N1, Boregowda H. S.1
1Department of Studies and Research in Mathematics, Jnanasiri Campus, Tumkur University, Tumakuru-572118, India
2Department of Mathematics, GFGC, Madhugiri-572132, India
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