Some properties of open subset intersection graph of a topological space

Abstract

In the recent paper, authors introduced a graph topological structure, called open subset intersection graph of a topological space ϒ(τ) on a finite set X. In this present paper, we continue the study of the graph ϒ(τ) on a finite set X. It is shown that, if τ is a discrete topology on X and |X| ≥ 3, then the graph ϒ(τ) is not bipartite and regular. If τ is a discrete topology on X with |X| = 3 then it is shown that the ϒ(τ) is an edge-transitive graph, Perfect graph, Eulerian and Hamiltonian graph . Moreover, we detremine exact value of the independence number, vertex connectivity and edge connectivity of the graph ϒ(τ).