This is a comprehensive book specifically aimed at undergraduate & postgraduate students of different Universities globally. Adopted a straight forward, example based approach with adequate number of exercise to clear up the confusion of reader. Included a number of important examples in Graph Theory demonstrating how one can solve problems of combination rather easily using Graph Theory. We believe the book would prove to be an extremely useful to students as well as to teachers as a ready reckon-er of the on Graph Theory. All definitions are accompanied with example for easy understanding. Hints are given for many problems and readers are invited to solve them using the hint. By doing this, we tried to ensure the active participation of a serious reader. Readers are facilitated by a detail index appended at end of the book. Also we shall entertain constructive criticise and suggestion towards the improvement of the book.