Applied Graph TheoryApplied Graph Theory provides an introduction to the fundamental concepts of graph theory and its applications. The five key topics that are covered in depth are: (i) foundations of electrical network theory; (ii) the directed-graph solutions of linear algebraic equations; (iii) topological analysis of linear systems; (iv) trees and their generation; and (v) the realization of directed graphs with prescribed degrees. Previously, these results have been found only in widely scattered and incomplete journal articles and institutional reports. This book attempts to present a unified and detailed account of these applications. A special feature of the book is that almost all the results are documented in relationship to the known literature, and all the references which have been cited in the text are listed in the bibliography. Thus, the book is especially suitable for those who wish to continue with the study of special topics and to apply graph theory to other fields. |
Contents
| 1 | |
| 36 | |
CHAPTER 3 Directedgraph solutions of linear algebraic equations | 140 |
CHAPTER 4 Topological analysis of linear systems | 224 |
CHAPTER 5 Trees and their generation | 320 |
CHAPTER 6 The realizability of directed graphs with prescribed degrees | 398 |
| 464 | |
| 473 | |
| 478 | |
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Common terms and phrases
2-trees applied associated associated directed graph assume basis branch called CHEN circuit Coates graph cofactor columns complete components compute connected connected graph consider consisting contains COROLLARY corresponding cotrees defined DEFINITION denoted determinant directed circuits directed graph directed trees discussed edges electrical network elements equal equicofactor matrix equivalent evaluation example exists expansion fact first follows formulas function given graph G graph obtained identity illustration incidence independent integers least Lemma length Let G linear major Mason graph matrix necessary nonsingular obtained operation orientation pairs partitions possible presented Problem procedure proof Prove realizable reduced reference node removing represented respectively result self-loops sequence shown in fig Similarly simply solution subgraph submatrix subset symbol symmetric terminal Theorem theory transformation unique voltage weight zero