Graph Theory, a branch of mathematics that studies the relationships between vertices and edges, has found widespread applications in various engineering disciplines. Its ability to model complex systems, represent relationships between components, and optimize processes makes it an invaluable tool in problem-solving. This paper explores the diverse applications of graph theory in engineering, from structural analysis and electrical networks to communication systems and transportation logistics. The paper discusses fundamental concepts in graph theory, such as trees, graphs, paths and cycles and demonstrates how these concepts are utilized in solving real-world engineering challenges. Furthermore, it highlights current trends, challenges, and future directions for research in this rapidly evolving field.