some dominating results of the join and corona operations between discrete topological graphs

The dominating sets play an important role in applications of graph theory. in this field, some recent studies discussed the properties of the minimum dominating set (γ-set). the other type of study produces a topological space from the set of vertices or the set of edges of a graph. the previous paper introduces a new method to construct a graph gτ from the topological space. in this paper, the dominating set and the domination number of gτ are proved with their inverse. the domination number and inverse domination number of corona operation and join operation between two graphs are discussed.