Topological domination in graph theory

Dominating sets play an important role in applications of graph theory. Recent studies in this field studied properties of minimum dominating sets (γ-set). The other type of studies produces a topology space from the set of vertices or the set of edges of a graph G. In this paper, the domination topology (τd) has been created form the set of minimal dominating sets of a graph G. The family of all minimal dominating sets (MDS) represents open sets in τd. The (∧d) d-intersection and (∨d) d-union have been defined.