Graph Theory has become an important discipline in its own right because of its applications to Computer Science, Communication Networks, and Combinatorial optimization through the design of efficient algorithms. It has seen increasing interactions with other areas of Mathematics. Although this book can ably serve as a reference for many of the most important topics in Graph Theory, it even precisely fulfills the promise of being an effective textbook. The main attention lies to serve the students of Computer Science, Applied Mathematics, and Operations Research ensuring fulfillment of their necessity for Algorithms. In the selection and presentation of material, it has been attempted to accommodate elementary concepts on essential basis so as to offer guidance to those new to the field.