Theory and Applications of Fermatean Neutrosophic Graphs

Said  Broumi; R.  Sundareswaran; M.  Shanmugapriya; Assia  Bakali; Mohamed  Talea

Authors

Said Broumi Laboratory of Information Processing, Faculty of Science Ben Mâ€™Sik, University of Hassan II, Casablanca, Morocco
R. Sundareswaran Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, India
M. Shanmugapriya Department of Mathematics, Sri Sivasubramaniya Nadar College of Engineering, India
Assia Bakali Ecole Royale Navale-Boulevard Sour Jdid, B.P 16303 Casablanca, Morocco
Mohamed Talea Laboratory of Information Processing, Faculty of Science Ben Mâ€™Sik, University of Hassan II, Casablanca, Morocco.

Keywords:

Pythagorean Fuzzy sets, Fermatean Fuzzy sets, Fermatean Neutrosophic sets, Fermatean Neutrosophic graphs

Abstract

Yager et. al. defined a q-rung orthopair fuzzy sets as a new general class of Pythagorean fuzzy set in which the sum of the qth power of the support for and support against is bonded by one. Tapan et. al. extended the concept of intuitionistic fuzzy sets as 3-rung orthopair fuzzy sets or Fermatean fuzzy sets (FFSs). Later C. Antony et. al. introduced the concept of Fermatean Neutrosophic Sets. In this work, we define Fermatean neutrosophic graphs and present some
operations on Fermatean neutrosophic graphs. Further, we introduce the concepts of regular Fermatean neutrosophic graphs, strong Fermatean neutrosophic graphs, Cartesian, Composition, Lexicographic product of Fermatean neutrosophic graphs. Finally, we give the applications of Fermatean neutrosophic graphs.