UID:
almahu_9949225539002882
Format:
1 online resource (499 p.)
ISBN:
0-444-60193-7
Series Statement:
North-Holland series in applied mathematics and mechanics ; v. 13
Content:
Applied Graph Theory
Note:
Sole distributors for the U.S.A.: American Elsevier Pub. Co., New York.
,
Front Cover; Applied Graph Theory; Copyright Page; Dedication; Preface; Table of Contents; CHAPTER 1. Basic theory; 1. Introduction; 2. Basic concepts of abstract graphs; 3. Operations on graphs; 4. Some important classes of graphs; 5. Directed graphs; 6. Mixed graphs; 7. Conclusions; Problems; CHAPTER 2. Foundations of electrical network theory; 1. Matrices and directed graphs; 2. The electrical network problem; 3. Solutions of the electrical network problem; 4. Invariance and mutual relations of network determinants and the generalized cofactors; 5. Invariance and the incidence functions
,
6. Topological formulas for RLC networks7. The existence and uniqueness of the network solutions; 8. Conclusions; Problems; CHAPTER 3. Directed-graph solutions of linear algebraic equations; 1. The associated Coates graph; 2. The associated Mason graph; 3. The modifications of Coates and Mason graphs; 4. The generation of subgraphs of a directed graph; 5. The eigenvalue problem; 6. The matrix inversion; 7. Conclusions; Problems; CHAPTER 4. Topological analysis of linear systems; 1. The equicofactor matrix; 2. The associated directed graph; 3. Equivalence and transformations
,
4. The associated directed graph and the Coates graph5. Generation of directed trees and directed 2-trees; 6. Direct analysis of electrical networks; 7. Conclusions; Problems; CHAPTER 5. Trees and their generation; 1. The characterizations of a tree; 2. The codifying of a tree-structure; 3. Decomposition into paths; 4. The Wang-algebra formulation; 5. Generation of trees by decomposition without duplications; 6. The matrix formulation; 7. Elementary transformations; 8. Hamilton circuits in directed-tree graphs; 9. Directed trees and directed Euler lines; 10. Conclusions; Problems
,
CHAPTER 6. The realizability of directed graphs with prescribed degrees1. Existence and realization as a (p, s)-digraph; 2. Realizability as a symmetric (p, s)-digraph; 3. Unique realizability of graphs without self-loops; 4. Existence and realization of a (p, s)-matrix; 5. Realizability as a weighted directed graph; 6. Conclusions; Problems; Bibliography; Symbol index; Subject index
,
English
Additional Edition:
ISBN 0-7204-2362-7
Language:
English
Bookmarklink