Fuzzy set theory was first introduced by Zadeh [7] in 1965. In 1994, Zhang [8] introduced the concept of bipolar fuzzy sets as a
generalization of fuzzy sets. Bipolar fuzzy sets are extensions of fuzzy sets whose range of membership degree is[−1, 1]. In Bipolar
fuzzy sets membership degree 0 of an element means that the element is irrelevant to the respective property, a positive membership
degree of an element indicates that the element somewhat satisfies the property and a negative membership degree of an element
indicates the element somewhat satisfies the implicit counter property. Several studies on bipolar fuzzy graphs [3, 4, 5, 6] were
occurred. Sunil M.P. and J. Sureshkumar [1, 2] studied sum distance in fuzzy graphs.
