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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.
Hanan Omar Zomam (Mon,) studied this question.
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