Abstract
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(t ) on a finite set X. In the present paper, we continue the study of the open subset inclusion graph of a topological space j(t ) on a finite set X regarding some important properties. It is shown that, if (X,t ) is a discrete topological space and |X|= 3, then the graph j(t ) is bipartite, regular, distance transitive, distance regular, Hamiltonian as well as vertex and edge-transitive. Also if (X,t ) is a discrete topological space and |X|= 3 then the graph j(t ) has a perfect matching and vertex connectivity and edge connectivity 2.
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