SUPOUT TOPOLOGY ON DIRECTED FUZZY GRAPHS

In this work, we introduce a topology, called supout topology and denoted $\mathcal{F}^{o}_{\mathcal{G}}$, for a fuzzy directed graph. We study some properties of this topology and give some examples of open and closed sets. We demonstrate that two isomorphic fuzzy directed graphs have homeomorphic supout topologies. In addition, we prove that this topology is an Alexandroff one and then use minimal basis to characterize homeomorphic fuzzy directed graphs. Finally, we investigate the connectedness of this topology vs. the connectivity of the graph.