Certain operations on m-polar picture fuzzy graphs

Abstract

Fuzzy graphs and their extensions, including m-polar fuzzy graphs and mpolar intuitionistic fuzzy graphs, find significant applications in various systems. The uncertainties in everyday life, stemming from inconsistent information, pose challenges for accurate modeling using existing techniques. To tackle this, researchers have introduced m-polar picture fuzzy graphs (mP P F G), a novel approach that addresses indeterminate and inconsistent information in real-valued problems. The paper presents several important operations like, Cartesian product, compositions, union, join, direct product, semi strong product and strong product of mP P F Gs along with various properties and theorems. Also, product mP P F G, complete product mP P F G are defined. The concepts of ring sum of two product mP P F Gs are also studied.