Chen / Lauwerier / Koiter Applied Graph Theory

Graphs and Electrical Networks
2. Auflage 2014
ISBN: 978-1-4831-6415-1
Verlag: Elsevier Science & Techn.
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band Volume 13, 558 Seiten, Web PDF

Reihe: North-Holland Series in Applied Mathematics and Mechanics

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.

Autoren/Hrsg.

Chen, Wai-Kai

Lauwerier, H. A.

Koiter, W. T.

Inhaltsverzeichnis

1;Front Cover;1
2;Applied Mathematics and Mechanics: Graphs and Electrical Networks;4
3;Copyright Page;5
4;Table of Contents;14
5;Dedication;6
6;PREFACE;8
7;PREFACE TO THE SECOND EDITION;11
8;CHAPTER 1. Basic theory;18
8.1;1. Introduction;18
8.2;2. Basic concepts of abstract graphs;20
8.3;3. Operations on graphs;30
8.4;4. Some important classes of graphs;34
8.5;5. Directed graphs;40
8.6;6. Mixed graphs;49
8.7;7. Conclusions;49
8.8;Problems;50
9;CHAPTER 2. Foundations of electrical network theory;53
9.1;1. Matrices and directed graphs;54
9.2;2. The electrical network problem;75
9.3;3. Solutions of the electrical network problem;79
9.4;4. Invariance and mutual relations of network determinants and the generalizedcofactors;94
9.5;5. Invariance and the incidence functions;124
9.6;6. Topological formulas for RLC networks;128
9.7;7. The existence and uniqueness of the network solutions;142
9.8;8. Conclusions;149
9.9;Problems;150
10;CHAPTER 3. Directed-graph solutions of linear algebraic equations;157
10.1;1. The associated Coates graph;158
10.2;2. The associated Mason graph;184
10.3;3. The modifications of Coates and Mason graphs;206
10.4;4. The generation of subgraphs of a directed graph;216
10.5;5. The eigenvalue problem;223
10.6;6. The matrix inversion;227
10.7;7. Conclusions;233
10.8;Problems;233
11;CHAPTER 4. Topological analysis of linear systems;241
11.1;1. The equicofactor matrix;242
11.2;2. The associated directed graph;247
11.3;3. Equivalence and transformations;268
11.4;4. The associated directed graph and the Coates graph;279
11.5;5. Generation of directed trees and directed 2-trees;286
11.6;6. Direct analysis of electrical networks;298
11.7;7. Conclusions;328
11.8;Problems;329
12;CHAPTER 5. Trees and their generation;337
12.1;1. The characterizations of a tree;337
12.2;2. The codifying of a tree-structure;342
12.3;3. Decomposition into paths;347
12.4;4. The Wang-algebra formulation;349
12.5;5. Generation of trees by decomposition without duplications;370
12.6;6. The matrix formulation;382
12.7;7. Elementary transformations;390
12.8;8. Hamilton circuits in directed-tree graphs;396
12.9;9. Directed trees and directed Euler lines;401
12.10;10. Conclusions;406
12.11;Problems;407
13;CHAPTER 6. The realizability of directed graphs with prescribed degrees;415
13.1;1. Existence and realization as a (/?, 5)-digraph;415
13.2;2. Realizability as a symmetric (/?, s)-digraph;444
13.3;3. Unique realizability of graphs without self-loops;457
13.4;4. Existence and realization of a (/?, s)-matrix;465
13.5;5. Realizability as a weighted directed graph;469
13.6;6. Conclusions;471
13.7;Problems;472
14;CHAPTER 7. State equations of networks;481
14.1;1. State equations in normal form;481
14.2;2. Procedures for writing the state equations;489
14.3;3. The explicit form of the state equation;497
14.4;4. An alternative representation of the state equation;507
14.5;5. Physical interpretations of the parameter matrices;508
14.6;6. Order of complexity;516
14.7;7. Conclusions;531
14.8;Problems;532
15;Bibliography;535
16;Symbol index;546
17;Subject index;552