Graph theory is a subject which is gaining momentum in the syllabi of different Engineering, streams especially in Electrical Engineering, Computer Science, Information Technology, Communication Engineering , Environmental science & Material Physics. The book is tailor made to the needs of students of undergraduate courses in Mathematics, B.Tech, and Post Graduate courses in science and computer application of various universities. The topics covered in the book have been chosen with a view to easily bridging the knowledge gap in Mathematics that exist between students of various streams for a better understanding of the subject. However the book gives a compact yet rigorous treatment of the mathematical tool available for a general of study of graphs. The book is also designed to be self contained consisting of eight chapters. Each chapter contains a large number of illustrations with examples to explain definitions and theorems therein. To stimulate further learning interest, practice problem are inserted.