Cubic bipolar fuzzy graphs with applications

Recently, Jun et al. have introduced the concept of cubic set as a generalization of the concept of fuzzy set and that of the interval valued fuzzy set. This concept has been widely applied in many circumstances like pattern recognition, decision making etc. So far, no attention has been paid towards graph of cubic set therefore leads us in this manuscript to study the concepts of interval valued bipolar fuzzy graph (IVBFG) and cubic bipolar fuzzy graph (CBFG). Some graph theoretic terms for CBFGs are defined along with the several operations. Illustrative examples are provided to explain the defined terms and several results are discussed. As application, a cubic bipolar fuzzy influence graph in a social group is elaborated.