Graph theory is considered to be a crucial analysis tool in computer science and mathematics. Due to the built-in simplicity of graph theory, it can be employed to model several distinct physical and abstract systems like transportation and communication networks, models for business administration, psychology, and political science and so on. The aim of this book is not just to describe the present state and development tendencies of this theory, but to educate the reader enough to enable him/her to embark on the research complications of their own. Taking into consideration the huge amount of knowledge regarding graph theory and practice are elucidated in this book, it focuses on primary topics of theoretical researches. This book intends to serve as a valuable source of reference for students associated with various fields like system sciences, engineering, social sciences, mathematics, computer sciences, etc. as well as for practitioners and software professionals.