Graph theory has emerged out as an important subject of study for the student of all branches of BTech courses, MCA and MSc (Mathematics and Computer Science), MTech in Computer Science due to its use in solving complicated problems in science, society, net-working and in making circuit in computer. The book has been written to provide a text book in the above mentioned courses. The book contains the details of definitions , theorems and applications. Adequate sketches and solved examples given in the book will be very much helpful to the student to understand the subject and open the applications. All algorithms of graph theory, tree and tree traversals are well explained with good examples. Euler’s and Hamiltonian graphs, graph colouring, chromatic polynomials, matrix representation of graphs and its uses in isomorphism are of special interest. The presentation is lucid, supported by sketches and examples will be of much interest to the students. About 110 objective type questions with solutions are added at the end to test the knowledge acquired by the reader.