The transportation problem is also one of the important problems in the field of optimization in which the goal is to minimize the total transportation cost of distributing to a specific number of sources to a specific number of destinations. Different techniques have been developed in the literature for solving the transportation problem. Specific methodologies concentrated on finding an initial basic feasible solution and the other to find the optimal solution. This manuscript analyses method of the optimal solution for the transportation problem utilizing a Bipartite graph. This procedure contains topological spaces, graphs, and transportation problems. Initially, it converts the transportation problem into a graphical demonstration then transforms into a new graphical image. Afterward using the proposed algorithmic rule we've obtained the optimal cost of transporting quantities from providing vertices to supply vertices. The above approach shows that the relation between the transportation problem and graph theory and it initiates to search out the various kind of solutions to the transportation problem. This method is also to be noticed that, requires the least number of steps to reach optimality as compare the obtained results with other wellknown meta-heuristic algorithms. In the end, this method is illustrated with a numerical example.