TOPOLOGICAL SPACES GENERATED BY GRAPH

By

P. S. Gholap¹ and V. E. Nikumbh²

¹Department of Mathematics, LRDP Arts, Science and Commerce College, Rahuri-413705, (MS) India

²Department of Mathematics, PVP College of Arts, Science and Commerce, Pravaranagar-413713, (MS) India

Email:vinayaknikumbh@yahoo.co.in

(Received : July 01, 2021; In format : August 14, 2021, Revised in final form : March 27, 2022)

DOI: https://doi.org/10.58250/Jnanabha.2022.52101

Abstract

In this paper we discuss topological spaces generated by simple graphs using adjacency relation and non adjacency relation on vertices. We establish important results showing relations between complete graph and discrete topological space. We also discuss the topological spaces related to complete graphs, isomorphic graphs and study their properties. Further we discuss the interior and closure operators and their properties. Our motivation is to give an fundamental step toward linkage between topology and graph so as to study different aspects of graphs in terms of topological properties.

2020 Mathematical Sciences Classification: O5C10.

Keywords and Phrases: Graph Theory, topological spaces, interior operator and closure operator.