Abstract
In this paper, we study the odigraphic topology for a directed edges of a digraph. We give some properties of this topology, in particular we prove that is an Alexandroff topology and when two digraphs are isomorphic, their odigraphic topologies will be homeomorphic. We give some properties matching digraphs and homeomorphic topology spaces. Finally, we investigate the connectedness of this topology and some relations between the connectedness of the digraph and the topology .
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