Vertex covering in wireless sensor networks (WSNs) is essential for tasks like monitoring link failures and facility location, as well as clustering and data aggregation. WSNs consist of small sensor nodes that wirelessly sense the environment and transmit data, relying on multi-hop communication due to limited transmission ranges and obstacles. Security is paramount due to vulnerabilities like eavesdropping and spoofing, making monitoring network traffic with secure nodes crucial. Graph theory aids in solving WSN issues, with finding a minimum Vertex Cover (VC) pivotal for link monitoring by designating nodes in the VC as secure points. Weighted connected VC structures enable energy-efficient communication, forming virtual backbones based on node energy levels. We have covered the application of vertex cover in wireless sensor networks in this paper. Performance evaluations of techniques such as the dynamic thresholding search (DTS_MVC) for massive graphs and the hybrid genetic algorithm (HGA) for WCVC are key contributions. These techniques improve network monitoring’s robustness, scalability, and energy efficiency. Algorithm complexity evaluations that include time, message, and energy consumption show how useful they are in real-world applications. The findings highlight how advanced vertex cover algorithms can be used to create safe, cost-effective WSN infrastructures that are appropriate for Internet of Things (IoT) applications.