Application of Graph Theory in Real Life to Develop Routes

Abstract

Graph theory is a special part of discrete mathematics, in which we describe the relationship between points and lines. It plays a significant role in the field of science, engineering and technology. With the help of Graph theory, we plan to develop bus routes to pick up students and take them to school. We denote each stop as a vertex, and the route as an edge. In this research paper, we use the Hamiltonian path to represent the efficiency of including each vertex within the route. Whether visiting a water park, theme park, or zoo, we plan an efficient route to visit a selected attraction or all of the attractions. Each vertex within the graph is represented by a Hamiltonian path or circuit. The obtained result is efficient to elucidate the methodology.