About the book
This book is concerned with the use of algebraic techniques in the study of graphs. The aim is to translate properties of graphs into algebraic properties and then, using the results and methods of algebra, to deduce theorems about graphs.
It is fortunate that the basic terminology of graph theory has now become part of the vocabulary of most people who have a serious interest in studying mathematics at this level. A few basic definitions are gathered together at the end of this chapter for the sake of convenience and standardization. Brief explanations of other graph-theoretical terms are included as they are needed. A small number of concepts from matrix theory, permutation-group theory, and other areas of mathematics, are used, and these are also accompanied by a brief explanation.
The literature of algebraic graph theory itself has grown enormously since 1974, when the original version of this book was published. Literally thousands of research papers have appeared, and the most relevant ones are cited here, both in the main text and in the Additional Results at the end of each chapter. But no attempt has been made to provide a complete bibliography, partly because there are now several books dealing with aspects of this subject. In particular there are two books which contain massive quantities of information, and on which it is convenient to rely for ‘amplification and exemplification’ of the main results discussed here.