Some significant results on open subset inclusion graph of a topological space

摘要

In the recent paper R. A. Muneshwar and K. L. Bondar, introduced a graph topological structure, called open subset inclusion graph of a topological space j(tau) on a finite set X. In the present paper, we continue the study of the open subset inclusion graph of a topological space j(tau) on a finite set X regarding some important properties. It is shown that, if (X, tau) is a discrete topological space and vertical bar X vertical bar = 3, then the graph j(tau) is bipartite, regular, distance transitive, distance regular, Hamiltonian as well as vertex and edge-transitive. Also if (X, tau) is a discrete topological space and vertical bar X vertical bar = 3 then the graph j(tau) has a perfect matching and vertex connectivity and edge connectivity 2.