A study of competitions in different fields through graphs under bipolar picture fuzzy environment.

Recent developments in the theory of fuzzy graphs have led to many extensions for modeling real-world problems involving uncertainty. Among these, competition graphs are crucial for representing competitive and ecological systems. In this study, the notion of bipolar picture fuzzy competition graphs, along with several generalizations including bipolar picture fuzzy k-competition graphs, p-competition graphs, and m-competition graphs are introduced. Several characteristics of these newly established graphs are investigated. We also explore their structural properties and apply the models to real-world competitive scenarios using computational frameworks. A comparative study is conducted to demonstrate the improved efficiency of the proposed models over existing approaches.