The ideas and methods of graph theory penetrate deeper into both the classical fields of application of this theory, for example, in electrical engineering, and into new areas, such as sociology and medicine. The concepts of graph theory such as , , , . are widely used in applications. This book includes works of the most recent time, relating to some important sections of graph theory .. Most articles contain final results little known to our readers. The collection can be seen as a significant addition to the book F. Harari (, 1973). The book will interest a wide range of mathematicians and engineers involved in graph theory and its applications. Graduate students and senior students of technical universities and universities can use it as a teaching aid.