Complex fermatean neutrosophic graph and application to decision making

A new growing area of neutrosophic set (NS) theory called complex neutrosophic sets (CNS) provides useful tools for dealing with uncertainty in complex valued physical variables that are observed in the actual world. A CNS take values for the truth, indeterminacy and falsity membership functions in the complex plane's unit circle. In this research, a novel concept of complex fermatean neutrosophic graph (CFNG) is established. We proposed the order, size, degree and total degree of a vertex of CFNG. Also, we presented the primary operations such as complement, union, join, ring-sum and cartesian product of CFNG. Moreover, the concept of regular graph under complex fermatean neutrosophic environment is discussed. Finally, an application of multi criteria decision making problem in educational system to evaluate lecturer’s research productivity using CFNG is discussed.