This paper explores the Minimum Dominating Set (MDS) problem, focusing on developing and applying an algorithm suited to different graph structures. The algorithm is tested on various graphs, including path, ladder, cycle, comb, binary trees, and sibling trees. Through extensive testing, the paper evaluates the algorithm’s performance in terms of solution quality, runtime efficiency, and scalability across diverse graph types. The findings provide valuable insights into algorithmic solutions for practical graph-based scenarios. Furthermore, the algorithm exhibits potential applications in fields such as facility location, surveillance, and network design, demonstrating its versatility and relevance in real-world contexts.