In the recent paper, R. A. Muneshwar et al., introduced a graph structure, called open subset inclusion graph j(t) of (X, t) . They also discussed a basic properties such as connectedness, diameter, girth, clique number, chromatic number, domination number, etc., of an open subset inclusion graph of a topological space. In this paper, we study some important results of the graph j(Tx × Ty) of a product topological space (X × Y, t). We also determine relationship between diameter, girth, clique number, chromatic number, domination number, degree etc., of the graphs j(Tx), j(Ty) and j(Tx × Ty).