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Theoretical concepts of graphs are highly utilized by computer science applications. Especially in research areas of computer science such as data mining, image segmentation, clustering, image capturing and networking. In this paper, we discussed some properties of the –complement of bipolar fuzzy graphs. Self –complement bipolar fuzzy graphs and self weak –complement bipolar fuzzy graphs are defined and a necessary condition for a bipolar fuzzy graph to be self –complement is given. We defined busy vertices and free vertices in bipolar fuzzy graphs and studied their image under an isomorphism. Categorical properties of bipolar fuzzy graphs are discussed. Also, we investigated some properties of isomorphism on bipolar fuzzy graphs.