| Description |
Algorithmic graph theory provides an interface between applied mathematics and computer science, with widespread applications that can be found throughout the sciences as well as in real-world systems and technologies. It concerns the study of relationships between objects, representing them with vertices and edges to create the graph data structure, along with various related algorithms and their complexities. We begin the paper with an introduction to relevant definitions and notations, then delve into different types of graphs and their properties. This is followed by an exploration of prominent problems in graph theory, introducing the shortest path problem, graph coloring problem, and minimum spanning tree problem. For each one we examine the algorithms frequently employed in solving this type of problem, then end with a practical application by explaining how the problem can be employed to model and solve a real-world issue. |
