Vol. 7, Issue 2, Part D (2025)

Wireless Sensor Networks (WSNs) have become essential infrastructures in environmental monitoring, industrial automation, military surveillance, and Internet of Things (IoT) applications. The core challenge in WSNs lies in ensuring long-term energy efficiency while maintaining robust network connectivity, given that sensor nodes operate with limited battery resources and often in inaccessible regions. Graph theory provides a rigorous mathematical framework for understanding, designing, and optimizing WSN architectures. This research review synthesizes studies from 2010 to 2025 and highlights how graph-theoretic models including unit disk graphs, random geometric graphs, dominating sets, spanning trees, and spectral graph methods are applied to enhance connectivity and energy efficiency.
The review discusses major graph-based strategies such as topology control, clustering protocols, energy efficient routing, graph sparsification, backbone construction, and the emerging role of Graph Neural Networks (GNNs). Results show that topology-control algorithms reduce node degree and conserve energy without sacrificing k-connectivity, clustering algorithms significantly decrease communication overhead, and energy-efficient routing prolongs network lifetime under various environmental constraints. Additionally, recent advancements in spectral methods and GNNs enable more adaptive, resilient, and optimized WSN topologies.