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Product of bipolar fuzzy graphs and their degree

The concepts of graph theory are applied in many areas of computer science including data mining, image segmentation, clustering, image capturing and networking. It is also known that lots of uncertainties occur in these areas. To handle the uncertainty that occurs in graph theory, fuzzy graph theory is successfully used in many problems. A bipolar fuzzy set is a generalization of the fuzzy set. In this paper, two new operations on bipolar fuzzy graphs, viz. normal product and tensor product, are defined. Also, the degrees of the vertices of the resultant graphs which are obtained from two given bipolar fuzzy graphs and using the operations Cartesian product, composition, tensor and normal product are determined.