ABSTRACT
One good example of the usefulness of graph theory is in scheduling the flights for an airline traveling to a set of cities in a way that will minimize the traveling costs involved. This is an optimization problem where the initial solution is obtained by reducing the problem to a graph. Here, the nodes are the cities where the planes travel while the edges are the traveling costs involved. The traveling costs between the cities vary according to factors such as time, duration, and other operational costs. In order to minimize the total traveling costs, the planes need to be scheduled according to priority order by considering the costs involved. A reduction of this priority order into the form of a graph is the first step.
