Graph theory is a well-known area of Discrete Mathematics which has so many theoretical developments and applications not only to different branches of Mathematics, but also to various other fields of basic sciences, technology, social sciences and computer science. Graphs are widely used as efficient and effective tools to model many types of practical and real-world problems in physical, biological, social and information systems.

In these lecture notes, I have mentioned several open problems that have gained respect among the researchers like Connectivity of Graphs, Tours and Matchings, Colourings, Graphs on Surfaces and Directed Graphs. The book will be useful for undergraduate and post graduate students.

Dr. Pritesh Andharia is an assistant professor in Mathematics Department of Institute of Computer Technology, Ganpat University located at Ganpat Vidyanagar, Mehsana district of Gujarat. He has completed his Ph.D. from Saurashtra University, Rajkot, Gujarat with specialization in Graph Theory. During his Ph.D., he introduced a new kind of graph labeling technique. This new graph labeling technique is included by Joseph Gallian in his Dynamic Survey on Graph Labeling. His research articles have been appeared in various SCOPUS/WOS/UGC-CARE/Peer Reviewed national and international journals like Mathematical Journal of Interdisciplinary  Sciences, Journal of Calcutta Mathematical Society, Global Journal of Pure and Applied Mathematics, IOSR Journal of Mathematics, TWMS Journal of Applied and Engineering Mathematics.