Some properties of open subset intersection graph of a topological space

摘要

In the recent paper, authors introduced a graph topological structure, called open subset intersection graph of a topological space gamma(tau) on a finite set X. In this present paper, we continue the study of the graph gamma(tau) on a finite set X. It is shown that, if tau is a discrete topology on X and vertical bar X vertical bar = 3, then the graph gamma(tau) is not bipartite and regular. If tau is a discrete topology on X with vertical bar X vertical bar = 3 then it is shown that the gamma(tau) 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 gamma(tau).