Binary Operations on Directed Fuzzy Graphs

In this paper, the newly directed fuzzy graphs are generated using the operations such as union, join, composition and cartesian product of two directed fuzzy graphs, accompanied by their illustrative analysis. The degree of vertices in the newly generated directed fuzzy graphs is defined, and properties based on vertex degree are established. Additionally, the degrees of corresponding vertices in the composition and cartesian product of two directed fuzzy graphs are compared. The orientation of defined operations on fuzzy graphs is compared with the corresponding operations on directed fuzzy graphs and analyzed through illustrative examples.