Graph-Theoretic Optimization of Backbone Structures in Wireless Sensor Networks Using Domination Models

Abstract Objectives: This study proposes an energy-aware backbone optimization framework for Wireless Sensor Networks (WSNs) to address the limitations of conventional single Connected Dominating Set (CDS)-based approaches, particularly in terms of adaptability, fault recovery, and uneven energy depletion among nodes. Method: A graph-theoretic model based on domination graphs is introduced, where each vertex represents a feasible dominating set and edges correspond to valid single-node transitions between backbone configurations. An energy-driven objective function guides these transitions, enabling progressive movement toward balanced states. The framework incorporates localized reconfiguration mechanisms and is supported by theoretical guarantees on connectivity preservation and convergence. Findings: Simulation-based evaluation demonstrates that the proposed framework achieves 18–25% improvement in network lifetime, 22% reduction in energy variance among backbone nodes, and 30% decrease in reconfiguration overhead compared to traditional CDS-based methods. Additionally, fault recovery time is reduced by approximately 35% due to localized transition mechanisms, eliminating the need for global recomputation. The model ensures stable convergence to energy-balanced configurations under dynamic network conditions, while maintaining full connectivity and coverage. Novelty: This work introduces a fundamentally new perspective by modelling the entire space of dominating sets as a structured domination graph, explicitly capturing both configurations and their transition pathways. Unlike existing approaches that rely on static or limited backbone structures, the proposed framework enables continuous, energy-aware navigation across multiple backbone states. This represents a significant advancement by integrating domination theory with dynamic optimization, providing a scalable and mathematically grounded solution for adaptive backbone management in WSNs. Keywords: Domination graph framework, Wireless sensor networks (WSNs), Connected dominating set (CDS), Energy-aware backbone optimization, Fault-resilient reconfiguration