Domination on Bipolar Fuzzy Graph Operations: Principles, Proofs, and Examples

Bipolar fuzzy graphs, capable of capturing situations with both positive and negative memberships, have found diverse applications in various disciplines, including decision-making, computer science, and social network analysis. This study investigates the domain of domination and global domination numbers within bipolar fuzzy graphs, owing to their relevance in these aforementioned practical fields. In this study, we introduce certain operations on bipolar fuzzy graphs, such as intersection, join, and union of two graphs. Furthermore, we analyze the domination number and the global domination number for various operations on bipolar fuzzy graphs, including intersection, join, and union of fuzzy graphs and their complements.