Presents a uniform approach to various engineering problems, such as analysis and synthesis of electrical networks, sampled-data feedback, control systems, switching networks, and communications nets.

In this book we attempt to develop the fundamental results of resistive network analysis, based upon a sound mathematical structure. The axioms upon which our development is based are Ohm's Law, Kirchhoff's Voltage Law, and Kirchhoff's Current Law. In order to state these axioms precisely, and use them in the development of our network analysis, an elaborate mathematical structure is introduced, involving concepts of graph theory, linear algebra, and one dimensional algebraic topology. The graph theory and one dimensional algebraic topology used are developed from first principles; the reader needs no background in these subjects. However, we do assume that the reader has some familiarity with elementary linear algebra. It is now stylish to teach elementary linear algebra at the sophomore college level, and we feel that the require ment that the reader should be familiar with elementary linear algebra is no more demanding than the usual requirement in most electrical engineering texts that the reader should be familiar with calculus. In this book, however, no calculus is needed. Although no formal training in circuit theory is needed for an understanding of the book, such experience would certainly help the reader by presenting him with familiar examples relevant to the mathematical abstractions introduced. It is our intention in this book to exhibit the effect of the topological properties of the network upon the branch voltages and branch currents, the objects of interest in network analysis.

Outstanding introductory treatment, geared toward advanced undergraduates and graduate students who require knowledge of graph theory. The first nine chapters constitute an excellent overview; the remaining chapters are more advanced and provide material for a variety of courses. 1974 edition.

The theory of networks is a very lively one, both in terms of developments in the theory itself and of the variety of its applications. This book, based on the 1981 AMS Short Course on the Mathematics of Networks, introduces most of the basic ideas of network theory and develops some of these ideas considerably.

The fusion between graph theory and combinatorial optimization has led to theoretically profound and practically useful algorithms, yet there is no book that currently covers both areas together. Handbook of Graph Theory, Combinatorial Optimization, and Algorithms is the first to present a unified, comprehensive treatment of both graph theory and c

Applied Graph Theory: Graphs and Electrical Networks, Second Revised Edition provides a concise discussion of the fundamentals of graph and its application to the electrical network theory. The book emphasizes the mathematical precision of the concepts and principles involved. The text first covers the basic theory of graph, and then proceeds to tackling in the next three chapters the various applications of graph to electrical network theory. These chapters also discuss the foundations of electrical network theory; directed-graph solutions of linear algebraic equations; and topological analysis of linear systems. Next, the book covers trees and their generation. Chapter 6 deals with the realizability of directed graphs with prescribed degrees, while Chapter 7 talks about state equations of networks. The book will be of great use to researchers of network topology, linear systems, and circuitries.