Abstract
Recently, bipolar fuzzy graph is a growing research topic as it is the generalisation of fuzzy graphs. Let G be a non-trivial group and S be a non-empty subset of G such that not containing the identity element of G and S = S-1 = {s-1| s ∈ S}. The Cayley graph Γ = Cay (G, S) is the graph whose vertex set V(Γ) is G and edge set E(Γ) is {{g, gs}| g ∈ G, s ∈ S}. A non-empty subset S of G such that not containing the identity and S = S-1 is referred to as a Cayley subset of G, and the Cayley graph Γ = Cay (G, S) is referred to as a Cayley graph of G relative to S. In this paper, we introduce the concept of Cayley bipolar fuzzy graphs on the bipolar fuzzy groups. Also some properties of Cayley bipolar fuzzy graphs as connectivity and transitivity are provided.
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