Graph theory is the study of graphs that are created by using mathematical structures to model relations between objects from certain collection. The graphs serve as a mathematical model for any system possessing a binary relation. This book gives an in-depth study of the fundamentals of graph theory and its applications. It skilfully illustrates various forms of graphs to help students analyse and understand the concepts clearly, with precision. All mathematical notations are explained with the help of definitions given with each and every section of the book. The book is meticulously organised in 13 chapters which are well-supported with examples, algorithms and theorems relevant to them. Primarily intended as a textbook for the undergraduate and postgraduate students of mathematics and computer science, this book will be equally useful for the undergraduate students of engineering