Domination in (2,1)-Fuzzy Graphs and Its Application

The notion of a fuzzy graph (FG) and its expanded variations have been devised to address several real-world issues including imprecision, such as decision-making, networking, shortest path, and so forth. The generalization of FG theory to circumstances where imprecision is characterized by differences in the values of membership and non-membership grades is the basis of this study. The purpose of this study is to present the (2,1)-fuzzy set graph concept. Furthermore, in a (2,1)-fuzzy environment, this study examines the idea of domination theory. More specifically, the theory related to (2,1)-fuzzy graphs is presented along with illustrative examples, introducing the framework. Additionally, the domination theory associated with (2,1)-fuzzy graphs is developed. Finally, a numeral example is presented to explain the computing of domination in (2,1)-fuzzy graph in the specific application.