Nowadays, the powerful combinatorial methods found in graph theory can be used to prove significant and well-known results in a variety of areas in mathematics. In this book, we present a few selected applications of graph theory to various operation research problems. Here, we have considered four classes of problems: transportation problem, dynamic networks problem, game theory and linear programming problem. These problems can be expressed and solved elegantly as graph theory problem involving connected and weight digraphs. From a practical point of view, all of these problems are trivial if the network is small. Many real-life situations, however, consist of huge networks, and therefore, it is important to solve these network problems by taking help of computers. We have developed some important algorithms and significant models to solve these problems in a simplified manner. The wide scope of these models and other applications has been well-documented.