Axler, F. Gehring, and K. This material is included here with the pennission of Gordon and Breaeh.
Graph theory. F68 5ll'. Use in connection with any form of information storage and retrieva1, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed is forbidden. The use of general descriptive names, trade names, trademarks, etc. The purpose of this book is to present selected topics from this theory that have been found useful and to point out various applications.
Graph theory applications - L. R. Foulds - Google книги
Some important theoretical topics have been omitted as they are not es-sential for the applications in Part II. Hence Part I should not be seen as a well-rounded treatise on the theory of graphs. Some effort has been made to present new applications that do not use merely the notation and ter-minology of graphs but do actually implement some mathematical results from graph theory. It has been written for final undergraduate year or first year graduate students in engineering, mathematics, computer science, and operations research, as well as researchers and practitioners with an inter-est in graph theoretic modelling.
Suggested plans for the reading of the book by people with these interests are given later. The book comprises two parts. The first is a brief introduction to the mathematical theory of graphs. The second is a discussion on the applications of this material to some areas in the subjects previously mentioned. It is, of course, possi-ble to read only the first part to attempt to gain an appreciation of the mathematical aspects of graph theory.
However even the purest of mathe-maticians is strongly recommended to delve seriously into the second part.
This is because the theory of graphs and the applications of graphs are inextricably intertwined. Much of the mathematical theory of graphs has arisen out of attempts to solve practical problems. So to ignore the utility of graph theory is to ignore a major part of its importance.
It contains exercises which the reader is urged to try. As with all disciplines, you cannot master graph theory without getting your hands dirty. Graph theory is not a spectator sport! We begin with an introductory chapter which introduces a little historical background and the fundamental notions. It is assumed in all later chap-ters that the reader is familiar with this material. Chapter 2 is concerned with connectivity - a concept which is basic for many of the later chapters.
One of the most important classes of graphs is that of trees and this is dealt with in Chapter 3. The material in the next chapter, on traversability, is of theoretical interest in its own right but is also of practical importance in operations research, covered in Chapter Chapter 5, on planarity, illustrates that the topic is more than just topology. It is necessary for the sections on layout in Chapter Chapter 6, on the matrices of a graph, is essential for a later discussion, on graph theoretic algorithms.
Chapter 7 is a necessarily brief account of directed graphs, called digraphs, and their im-portant special case; the network. Chapter 8, on covering, dominance, and matching has application in industrial engineering and other disciplines. Chapter 9 covers graph theoretic algorithms. In Chapter 10 we make a brief excursion into the world of matroids, where there are applications in electrical engineering, among other areas. Part II has mainly longer chap-ters explaining the application of the above-mentioned material in various branches of engineering, operations research, and science.
No attempt has been made to make this part encyclopaedic. Rather, due to limititations of space and for other reasons, just a few applications have been presented in some depth.
They are intended to give some impression of the power and wide utility of graph theory. Other one-semester sequences are given later. These require a greater level of mathematical maturity.
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Publisher: Springer , This specific ISBN edition is currently not available. View all copies of this ISBN edition:. Synopsis About this title The first part of this text covers the main graph theoretic topics: connectivity, trees, traversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids.
Review : L. Foulds Graph Theory Applications "This book put[s] together the theory and applications of graphs in a single, self-contained, and easily readable volume. Buy New Learn more about this copy. Other Popular Editions of the Same Title. Search for all books with this author and title. Customers who bought this item also bought. Stock Image.
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