This book is based on a course Graph theory. We write this book as per the revised syllabus of F.Y. B.Sc.(Computer Science) Mathematics, revised by Savitribai Phule Pune University, Pune, implemented from June 2019. Graph theory is the most useful subject in all branches of mathematics and it is used extensively in applied mathematics and engineering. Graphs theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects. It is a bridge connecting mathematics with various branches of computer science. We study how problems in almost every conceivable discipline can be solved using graph models.