Equitable Domination in Turiyam Graphs with Network Applications

Background Turiyam graphs provide a mathematical framework for representing systems with uncertainty, inconsistency, incomplete information, and refusal conditions. This study introduces the concept of equitable domination in Turiyam graphs to achieve balanced dominance among neighboring vertices and reduce excessive dependence on individual nodes in uncertain network structures. Methods The study defines equitable dominating sets in Turiyam graphs and investigates their theoretical properties. Relationships between equitable domination and classical domination concepts are examined through mathematical analysis. Fundamental properties, bounds, and characterizations of equitable domination are established within the Turiyam graph framework. Results The analysis shows that equitable domination supports balanced control and efficient resource allocation in uncertain networks. Equitable dominating sets generally require a slightly larger number of dominating vertices than minimum dominating sets, but they provide improved balance, fault tolerance, and network stability. The study also identifies potential applications in communication systems, wireless sensor networks, cloud computing, and social interaction models where reliable connectivity and fair workload distribution are important. Conclusions Equitable domination in Turiyam graphs provides an effective approach for analyzing and designing complex systems operating under uncertain conditions. The proposed framework extends domination theory in generalized graph structures and offers a foundation for future studies on optimization, decision-making, and network management in uncertain environments.