Tracking Misinformation and Influence Spread in Social Networks Using Equitable Fair Power Domination in Fuzzy Graphs

Abstract

This paper investigates the concept of Equitable Fair Power Domination (EFPD) in fuzzy graphs, integrating power domination principles with equitable and fair domination strategies to enhance decision-making in network monitoring. The study systematically establishes fundamental properties, theoretical results, and numerical illustrations to provide a comprehensive understanding of optimal node selection for effectively tracking and controlling misinformation in complex social networks. By leveraging fuzzy graph structures, the proposed framework ensures balanced influence distribution, preventing dominance by a single entity and minimizing biases in fact-checking and decision-making processes. The theoretical formulations are validated through numerical computations, demonstrating how EFPD can be applied to strategically identify key influencers or misinformation sources within a network. The findings contribute significantly to the development of robust methodologies for social network analysis, cybersecurity, strategic communication, and misinformation control, ensuring fairness and efficiency in information dissemination and verification.