Digraphs: Theory, Algorithms and Applications
Description:The study of directed graphs has developed enormously over recent decades, yet no book covers more than a tiny fraction of the results from more than 3000 research articles on the topic. Digraphs is the first book to present a unified and comprehensive survey of the subject. In addition to covering the theoretical aspects, including detailed proofs of many important results, the authors present a number of algorithms and applications. The applications of digraphs and their generalizations include among other things recent developments in the Travelling Salesman Problem, genetics and network connectivity. More than 700 exercises and 180 figures will help readers to study the topic while open problems and conjectures will inspire further research. This book will be essential reading and reference for all graduate students, researchers and professionals in mathematics, operational research, computer science and other areas who are interested in graph theory and its applications.
Good for experts and researchers but not for beginners
I come across this book when finding relevant materials of graph theory. As told by previous reviewer, this book contains much recent research results and is good for experts or researchers. The preface says that it is suitable for undergraduate, but in my feeling, you need to be a graduate with a full year course of graph theory completed to understand or utilize the materials of the book. The materials are presented in a standard theorem-proof format, one theorem after another. Examples are few. Though the book title contains `Algorithm`, there are also few algorithms presented in the form you saw in books of computing. Probably you need to design your own algorithm after digesting the material. Besides, exercises are abundant but no hints or answers provided.
Directed graphs are more general than undirected graphs
This book reflects the main achievements of the last three decades in the directed graphs theory as well as many applications including combinatorial optimization, operations research and the fascinating area of mathematics and computer science called discrete mathematics. Since the monograph contents are given, I do not wish to go into details of material presented there. Instead I'd like to discuss the aims of the book as well as who could be its readers.
The text strives to accomplish the following objectives:
1. To give a great deal of information on both results and proof techniques for specialists in graph theory. No other book covers even 10% of material provided in Digraphs, and thus before this monograph has been published even specialists in graph theory very often needed to search for a specific result or proof technique through the ocean of literature on digraphs. Now the situation has drastically improved.
2. To introduce researchers and practitioners from various other fields in mathematics, computer science, operations research, biology, etc. to basic and more advanced results in digraph theory and algorithms and some carefully selected applications. It offers much more than merely a pure bibliography and provides the ideal starting point for any researcher who needs to become familiar either with theory oriented aspects of this interesting area or with some application in a relatively short time.
3. To provide enough material for intermediate and final year BSc or MSc courses for students in mathematics, computer science and operations research. The large number of exercises (more than 700) of various difficulty is of great help to instructors and lecturers. The applications provided in the book will help to provide enough motivation for the students to study digraph theory and algorithms.
4. To provide a large variety of topics for final year student projects in mathematics, computer science, operations research and other fields. The monograph can be used as a source for the projects because because several areas of digraph theory are covered there in real depth and they vary from relatively simple to reasonably complicated ones.
To summarize, I'd like to notice that the monograph is aimed to a wide range of readers including specialists in mathematics, operations research, computer science, biology, etc. as well as students of second year and higher.
Boris Goldengorin, Department of Econometrics and Operations Research, University of Groningen, The Netherlands