Enhancing Social Network Security Using Equitable Fair Edge Domination in Fuzzy Graphs

Abstract

In online social networks, cyber threats such as spam, phishing, and misinformation propagate through communication links, making security monitoring a critical challenge. Traditional approaches often lead to overburdening certain network connections, resulting in inefficient surveillance and increased vulnerability. To address this, we introduce the Fuzzy Regular Equitable Fair Domination Graph (FREFDG) and apply Equitable Fair Edge Domination (EFEDS) as a strategic model for balanced security monitoring. This framework ensures that security resources are distributed equitably across edges, thereby preventing overload and ensuring comprehensive threat detection. The theoretical foundations of EFEDS are rigorously established through propositions, theorems, and numerical illustrations, demonstrating its effectiveness in optimizing network surveillance. A decision-making model is formulated using graph-based analysis, enabling the systematic selection of critical edges requiring direct monitoring while leveraging indirect supervision for non-critical edges. This structured approach reduces computational complexity while enhancing network resilience. Additionally, we present a real-world application scenario, showcasing how EFEDS can be implemented in spam detection, phishing prevention, and misinformation filtering. The results demonstrate the efficiency of our framework in identifying high-risk edges, reducing redundant monitoring efforts, and improving threat mitigation strategies. By integrating fuzzy logic with equitable fair domination principles, our approach contributes to a more adaptive, scalable, and intelligent cybersecurity model, offering valuable insights for network security experts and researchers.