Total Graphic Topology on the Vertex Sets of Directed Graphs

In this work, we introduce a topology T tot G , called the total graphic topology, for the vertices set of a directed graph G = (V, E).We prove many properties of this topology and we give some open sets and some closed ones.We prove that T tot G is an Alexandroff topology.In addition, we investigate functions between directed graphs, the connectedness of this topology for some strongly connected graphs and we give an example for each case.