An edition of Graph theory with applications to engineering and computer science (1974)

Graph theory with applications to engineering and computer science.

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Cover of: Graph theory with applications to engineering and computer science. by Narsingh Deo, Narsingh Deo, Narsingh Deo
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An edition of Graph theory with applications to engineering and computer science (1974)

Graph theory with applications to engineering and computer science.

by and

  • 5 Want to read
  • 2 Currently reading

This edition doesn't have a description yet. Can you add one?

Publish Date
Publisher
Prentice-Hall
Language
English
Pages
478

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Previews available in: English

Subjects

Graph theory, Engineering mathematics
Edition Availability
Cover of: Graph Theory with Applications to Engineering and Computer Science
Graph Theory with Applications to Engineering and Computer Science
2017, Dover Publications, Incorporated
in English
Cover of: Graph Theory with Applications to Engineering and Computer Science
Graph Theory with Applications to Engineering and Computer Science
2016, Dover Publications, Incorporated
in English
Cover of: Graph Theory with Applications to Engineering and Computer Science
Graph Theory with Applications to Engineering and Computer Science
October 15, 2004, Prentice-Hall of India Pvt.Ltd
Paperback - New Ed edition
Cover of: Graph theory with applications to engineering and computer science.
Graph theory with applications to engineering and computer science.
1974, Prentice-Hall
in English

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Book Details

Table of Contents

Preface
Page xv
1. Introduction
Page 1
1-1. What is a Graph?
Page 1
1-2. Application of Graphs
Page 3
1-3. Finite and Infinite Graphs
Page 6
1-4. Incidence and Degree
Page 7
1-5. Isolated Vertex, Pendant Vertex, and Null Graph
Page 8
1-6. Brief History of Graph Theory
Page 10
Summary
Page 11
References
Page 11
Problems
Page 12
2. Paths and Circuits
Page 14
2-1. Isomorphism
Page 14
2-2. Subgraphs
Page 16
2-3. A Puzzle With Multicolored Cubes
Page 17
2-4. Walks, Paths, and Circuits
Page 19
2-5. Connected Graphs, Disconnected Graphs, and Components
Page 21
2-6. Euler Graphs
Page 23
2-7. Operations On Graphs
Page 26
2-8. More on Euler Graphs
Page 28
2-9. Hamiltonian Paths and Circuits
Page 30
2-10. The Traveling Salesman Problem
Page 34
Summary
Page 35
References
Page 35
Problems
Page 36
3. Trees and Fundamental Circuits
Page 39
3-1. Trees
Page 39
3-2. Some Properties of Trees
Page 41
3-3. Pendant Vertices in a Tree
Page 43
3-4. Distance and Centers in a Tree
Page 45
3-5. Rooted and Binary Trees
Page 48
3-6. On Counting Trees
Page 52
3-7. Spanning Trees
Page 55
3-8. Fundamental Circuits
Page 57
3-9. Finding All Spanning Trees of a Graph
Page 58
3-10. Spanning Trees in a Weighted Graph
Page 61
Summary
Page 64
References
Page 64
Problems
Page 65
4. Cut-Sets and Cut-Vertices
Page 68
4-1. Cut-Sets
Page 68
4-2. Some Properties of a Cut-Set
Page 69
4-3. All Cut-Sets in a Graph
Page 71
4-4. Fundamental Circuits and Cut-Sets
Page 73
4-5. Connectivity and Separability
Page 75
4-6. Network Flows
Page 79
4-7. 1-Isomorphism
Page 80
4-8. 2-Isomorphism
Page 82
Summary
Page 85
References
Page 86
Problems
Page 86
5. Planar and Dual Graphs
Page 88
5-1. Combinatorial Vs. Geometric Graphs
Page 88
5-2. Planar Graphs
Page 90
5-3. Kuratowski's Two Graphs
Page 90
5-4. Different Representations of a Planar Graph
Page 93
5-5. Detection of Planarity
Page 99
5-6. Geometric Dual
Page 102
5-7. Combinatorial Dual
Page 104
5-8. More on Criteria of Planarity
Page 107
5-9. Thickness and Crossings
Page 108
Summary
Page 109
References
Page 110
Problems
Page 110
6. Vector Spaces of a Graph
Page 112
6-1. Sets with One Operation
Page 112
6-2. Sets with Two Operations
Page 116
6-3. Modular Arithmetic and Galois Fields
Page 118
6-4. Vectors and Vector Spaces
Page 120
6-5. Vector Space Associated with a Graph
Page 121
6-6. Basis Vectors of a Graph
Page 123
6-7. Circuit and Cut-Set Subspaces
Page 125
6-8. Orthogonal Vectors and Spaces
Page 129
6-9. Intersection and Join of W and Ws
Page 131
Summary
Page 134
References
Page 135
Problems
Page 135
7. Matrix Representation of Graphs
Page 137
7-1. Incidence Matrix
Page 137
7-2. Submatrices of A(G)
Page 141
7-3. Circuit Matrix
Page 142
7-4. Fundamental Circuit Matrix and Rank of B
Page 144
7-5. An Application to a Switching Network
Page 146
7-6. Cut-Set Matrix
Page 151
7-7. Relationships among Af, Bf, and Cf
Page 153
7-8. Path Matrix
Page 156
7-9. Adjacency Matrix
Page 157
Summary
Page 162
References
Page 162
Problems
Page 162
8. Coloring, Covering, and Partitioning
Page 165
8-1. Chromatic Number
Page 165
8-2. Chromatic Partitioning
Page 169
8-3. Chromatic Polynomial
Page 174
8-4. Matchings
Page 177
8-5. Coverings
Page 182
8-6. The Four Color Problem
Page 186
Summary
Page 190
References
Page 190
Problems
Page 192
9. Directed Graphs
Page 194
9-1. What Is a Directed Graph?
Page 194
9-2. Some Types of Digraphs
Page 197
9-3. Digraphs and Binary Relations
Page 198
9-4. Directed Paths and Connectedness
Page 201
9-5. Euler Digraphs
Page 203
9-6. Trees with Directed Edges
Page 206
9-7. Fundamental Circuits in Digraphs
Page 212
9-8. Matrices A, B, and C of Digraphs
Page 213
9-9. Adjacency Matrix of a Digraph
Page 220
9-10. Paired Comparisons and Tournaments
Page 227
9-11. Acyclic Digraphs and Decyclization
Page 230
Summary
Page 233
References
Page 234
Problems
Page 234
10. Enumeration of Graphs
Page 238
10-1. Types of Enumeration
Page 238
10-2. Counting Labeled Trees
Page 240
10-3. Counting Unlabeled Trees
Page 241
10-4. Polya's Counting Theorem
Page 250
10-5. Graph Enumeration With Polya's Theorem
Page 260
Summary
Page 264
References
Page 264
Problems
Page 265
11. Graph Theoretic Algorithms and Computer Programs
Page 268
11-1. Algorithms
Page 269
11-2. Input: Computer Representation of a Graph
Page 270
11-3. The Output
Page 273
11-4. Some Basic Algorithms
Page 274
Algorithm 1. Connectedness and Components
Page 274
Algorithm 2. A Spanning Tree
Page 277
Algorithm 3. A Set of Fundamental Circuits
Page 280
Algorithm 4. Cut-Vertices and Separability
Page 284
Algorithm 5. Directed Circuits
Page 287
11-5. Shortest-Path Algorithms
Page 290
Algorithm 6. Shortest Path from a Specified Vertex to Another Specified Vertex
Page 292
Algorithm 7. Shortest Path between All Pairs of Vertices
Page 297
11-6. Depth-First Search on a Graph
Page 301
Algorithm 8. Planarity Testing
Page 304
11-7. Algorithm 9: Isomorphism
Page 310
11-8. Other Graph-Theoretic Algorithms
Page 312
11-9. Performance of Graph-Theoretic Algorithms
Page 314
11-10. Graph-Theoretic Computer Languages
Page 316
Summary
Page 317
References
Page 318
Problems
Page 321
Appendix of Programs
Page 323
12. Graphs in Switching and Coding Theory
Page 328
12-1. Contact Networks
Page 329
12-2. Analysis of Contact Networks
Page 330
12-3. Synthesis of Contact Networks
Page 334
12-4. Sequential Switching Networks
Page 342
12-5. Unit Cube and Its Graph
Page 348
12-6. Graphs in Coding Theory
Page 351
Summary
Page 351
References
Page 354
Problems
Page 354
13. Electrical Network Analysis by Graph Theory
Page 356
13-1. What Is an Electrical Network ?
Page 357
13-2. Kirchhoff's Current and Voltage Laws
Page 358
13-3. Loop Currents and Node Voltages
Page 359
13-4. RLC Networks with Independent Sources: Nodal Analysis
Page 362
13-5. RLC Networks with Independent Sources: Loop Analysis
Page 371
13-6. General Lumped, Linear; Fixed Networks
Page 373
Summary
Page 379
References
Page 381
Problems
Page 381
14. Graph Theory in Operations Research
Page 384
14-1. Transport Networks
Page 384
14-2. Extensions of Max-Flow Min-Cut Theorem
Page 390
14-3. Minimal Cost Flows
Page 393
14-4. The Multicommodity Flow
Page 395
14-5. Further Applications
Page 396
14-6. More on Flow Problems
Page 397
14-7. Activity Networks in Project Planning
Page 400
14-8. Analysis of an Activity Network
Page 402
14-9. Further Comments on Activity Networks
Page 408
14-10. Graphs in Game Theory
Page 409
Summary
Page 414
References
Page 414
15. Survey of Other Applications
Page 416
15-1. Signal-Flow Graphs
Page 416
15-2. Graphs in Markov Processes
Page 424
15-3. Graphs in Computer Programming
Page 439
15-4. Graphs in Chemistry
Page 449
15-5. Miscellaneous Applications
Page 454
Appendix A. Binet-Cauchy Theorem
Page 458
Appendix B. Nullity of a Matrix and Sylvester's Law
Page 460
Index
Page 463

Edition Notes

Includes bibliographies.

Published in
Englewood Cliffs, N.J
Series
Prentice-Hall series in automatic computation

Classifications

Dewey Decimal Class
511/.5
Library of Congress
TA338.G7 D46, QA166

The Physical Object

Pagination
xvii, 478 p.
Number of pages
478

Edition Identifiers

Open Library
OL5415723M
Internet Archive
graphtheorywitha0000deon
ISBN 10
0133634736
LCCN
73007566
OCLC/WorldCat
624148
LibraryThing
393380
Goodreads
4798247

Work Identifiers

Work ID
OL5915720W

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Download catalog record: RDF / JSON / OPDS | Wikipedia citation
September 3, 2025 Edited by MARC Bot remove likely corrupt MARC source
June 15, 2024 Edited by Drini Add TOC from Tocky
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December 12, 2023 Edited by MARC Bot import existing book
April 1, 2008 Created by an anonymous user Imported from Scriblio MARC record