Several Parameters of Domination and Inverse Domination in Discrete Topological Graphs

Abstract

Let  be a topological graph where  is a set of all vertices of  and each vertex is represent a set of the topology  non-equal to  or . The set of all edges of  is  such that there is an edge between any two vertices if no one of their topological sets are subset from the other. In this paper, many bounds and properties of domination are studied and applied on the topological graph. Three types of domination parameters are studied: co-independent domination, complementary tree domination and bi-domination. The co-independent domination number of , denoted by , the complementary tree domination number of , denoted by  and the bi-domination number of , denoted by  are proved and found. Also, the inverse dominating set and inverse domination number for these types is calculated.