In this article, we'll look at some of the composition and joining procedures on fuzzy graphs that are most frequently used. Numerous studies have been conducted on this subject since the beginning and development of fuzzy set theory, and one outcome is the fuzzy graph. In this new field of study known as "Fuzzy Graph Theory," we investigated the concept of several operations, such as null anti-fuzzy graphs and the relationship between full anti-fuzzy graphs and strong anti-fuzzy graphs. There is a study of the various fuzzy relation types. On a fuzzy graph, operations like the Cartesian product, union, and join are examined. A fuzzy graph's attributes are looked at, including its complement, its full and partial sub graphs, the degrees and total degrees of its vertices, its full and partial regularity, its completeness, and its status as a tree