Some results on the open subset intersection graph of a product topological space

Abstract

In the recent paper, R. A. Muneshwar et al., introduced a graph structure called open subset intersection graph g(t)  on a topological space (X, t).  In this paper, we study some important results of a graph g(t)  of a product topological space (X × Y, t).  We also determine relationship between diameter, girth, clique number, chromatic number, domination number etc. of an open subset intersection graph of a topological space (X × Y, t), (X, tX) and  (Y, tY). Moreover, we proved that, if (X, tX)  and (Y, tY)  are discrete topological space then w(g(tX × tY)) = w(g(tX)) * w(g(tY)) – 2 and c(g(tX × tY)) = c(g(tX)) * c(g(tY)) – 2  and domination number of g(tX × tY)  is 2. We also determine diameter and girth of intersection Graph of Product Topology on X × Y  for different values of m and n.