Bipolar fuzzy graph structures, bipolar fuzzy -cycles and φ-complement of a bipolar fuzzy graph structure concepts are introduced and investigated. We also discuss in detail φ-complement of a bipolar fuzzy graph structure along with strong self complementary and self-complementary bipolar fuzzy graph structures. We also developed some other concepts on this topic and worked to add some theorems and examples of these new concepts.

bipolar fuzzy set, graph structure, bipolar fuzzy graph structure, strong bipolar fuzzy graph structure, bipolar -cycles, φ-complement of a bipolar fuzzy graph structure.