Author Profile

Robin J. Wilson is Professor Emeritus of Mathematics at Western Michigan University. He received his Ph.D. in mathematics from Michigan State University. His research is in the area of graph theory. Professor Wilson has authored or co-authored more than 275 research papers and a number of textbooks in discrete mathematics and graph theory as well as the textbook on mathematical proofs. He has given over 100 lectures at regional, national and international conferences and has been a co-director of many conferences. He has supervised 22 doctoral students and numerous undergraduate research projects and has taught a wide range of subjects in undergraduate and graduate mathematics. He is the recipient of the University Distinguished Faculty Scholar Award and the Alumni Association Teaching Award from Western Michigan University and the Distinguished Faculty Award from the State of Michigan. He was the first managing editor of the Journal of Graph Theory. He is a member of the Institute of Combinatorics and Its Applications, the American Mathematical Society, the Mathematical Association of America and the editorial boards of the Journal of Graph Theory and Discrete Mathematics.

About The Book

In recent years, graph theory has established itself as an important mathematical tool in a wide variety of subjects, ranging from operational research and chemistry to genetics and linguistics, and from electrical engineering and geography to sociology and architecture. At the same time it has also emerged as a worthwhile mathematical discipline in its own right. This book, Foundations of Graph Theory is born out of a passion for unraveling the elegance and utility of graphs. It aims to bridge the gap between theoretical foundations and practical applications, catering to students, researchers, and professionals alike. With its structured progression from introductory topics to advanced themes, the book serves as both an educational guide and a reference for exploring the depths of graph theory. Through its chapters, readers will journey from the rudiments of graph definitions and properties to specialized topics like magic labeling, graph coloring, and isomorphism. The exploration is not merely theoretical; real-world applications across disciplines are woven throughout to demonstrate the relevance and adaptability of graph theory. In recent years, graph theory has established itself as an important mathematical tool in a wide variety of subjects, ranging from operational research and chemistry to genetics and linguistics, and from electrical engineering and geography to sociology and architecture. At the same time it has also emerged as a worthwhile mathematical discipline in its own right. In view of this, there is a need for an inexpensive introductory text on the subject, suitable both for mathematicians taking courses in graph theory and also for nonspecialists wishing to learn the subject as quickly as possible. It is hoped that this book goes some way towards filling this need. The only prerequisites to reading it are a basic knowledge of elementary set theory and matrix theory, although a further knowledge of abstract algebra is needed for more difficult exercises.

Table of Contents

Preface
Chapter 1. Introduction to Graph Theory
Chapter 2. Graph Representations
Chapter 3. Graph Traversal Algorithms
Chapter 4. Trees and Tree Algorithms
Chapter 5. Graph Connectivity
Chapter 6. Graph Coloring
Chapter 7. Planar Graphs
Chapter 8. Eulerian and Hamiltonian Graphs
Chapter 9. Graph Isomorphism and Automorphisms
Chapter 10. Directed Graphs and DAGs
Bibliography