α-Domination in Fuzzy Graphs with Applications to Fake News Control

Abstract

The uncontrolled spread of misinformation across online social networks poses serious societal risks, including political manipulation, public health misinformation and erosion of public trust. Due to uncertainty in user interactions and varying influence levels, classical crisp graph models are often inadequate for realistic modeling. In this paper, we introduce an α-domination framework in fuzzy
graphs to model and control fake news propagation. We formally define fuzzy coverage via direct and two-step influence with decay and establish theoretical properties of the α-domination number, including upper bounds, monotonicity and results for complete fuzzy graphs. We demonstrate how strategically selected α-dominating sets can act as fact-checking nodes to effectively reduce misinformation spread. Our framework provides a mathematically rigorous and flexible tool for misinformation containment under uncertainty, bridging fuzzy graph theory and social network analysis.