ABSTRACT
Graph theory aids as a mathematical model to signify any scheme confining a binary relation. In this paper, the Assignment problem and Game theory are solved in symmetric and non-symmetric problems using the Graph Theory approach. The method proposed in this work is a methodical process, apparent to implement for resolving assignment problems and Game theory problems in which so many routes of the path are possible to find the optimal solution in the directed graph and undirected graph in Graph theory. In this proposed work, the main graph is used to frame three other sub-graphs. Four routes of the path are taken in different ways in the graph. For each route, there is an in-degree and out-degree which frames the matrix representation. A numerical specimen is examined by means of a new technique in addition, the solution is computed by the existing two methods. Also, a performance comparison is made for the optimum solutions amongst this new method besides the two prevailing methods by means of Matlab. Using the graph theory, the solution to the assignment problem and game theory can be determined. The present work finally concludes the frame of the matrix of indegree and outdegree and also the results of the Assignment problem and game theory can be obtained.
