Finite graphs and networks : an introduction with applications

308 p., fig.Here is a clear, extensive exposition of the fundamentals of the mathematical theory of linear graphs. Because of its nature and broad applicability, graph theory is useful to anyone engaged in, or preparing for, work in the general area of mathematics, science, engineering, or the behavioral sciences. This book is intended as an undergraduate or first-year graduate text, or for self-study. In simplest terms, a linear graph, as a tool for studying interrelationships between objects, may be regarded as a collection of points, some of which are joined in pairs by interconnecting lines. Graph theory deals with the local and global structural characteristics of such configurations, as well as additional classes of problems which may be posed when numerical characteristics (such as distances, costs, flows, probabilities, etc.) are associated with the points and/or lines, forming a model of some type of system which may be physical, social, or purely mathematical. This book introduces the basic theory itself, and a wide range of applications for which this theory is a useful tool ... applications particularly evident in Chapter six. Once the reader is aware of the wide variety of uses of graph theory, he can study in depth those aspects and applications of special significance to him. The book is divided into two major parts. Part I, Chapters 1-5, develops the basic theory; Part II, Chapters 6-7, applies the basic theory to a broad spectrum of physical problems plus to other related topics in mathematics itself. As each new concept is introduced, it is clarified with examples. In addition, numerous exercises, accompanied by answers and hints, are provided. A knowledge of basic concepts in set theory and a brief familiarity with vectors and matrices is all that is necessary for an understanding of this material