Graph theory with applications to engineering and computer science.
Series: Prentice-Hall series in automatic computation
Publisher: Prentice-Hall
Published: 1974
Place of publication: Englewood Cliffs, N.J
Language: eng
Number of pages: 478
Subjects: Graph theory
Notes: Includes bibliographies.
Table of contents: title: Preface
pagenum: xv; label: 1
title: Introduction
pagenum: 1; label: 1-1
title: What is a Graph?
pagenum: 1; label: 1-2
title: Application of Graphs
pagenum: 3; label: 1-3
title: Finite and Infinite Graphs
pagenum: 6; label: 1-4
title: Incidence and Degree
pagenum: 7; label: 1-5
title: Isolated Vertex, Pendant Vertex, and Null Graph
pagenum: 8; label: 1-6
title: Brief History of Graph Theory
pagenum: 10; title: Summary
pagenum: 11; title: References
pagenum: 11; title: Problems
pagenum: 12; label: 2
title: Paths and Circuits
pagenum: 14; label: 2-1
title: Isomorphism
pagenum: 14; label: 2-2
title: Subgraphs
pagenum: 16; label: 2-3
title: A Puzzle With Multicolored Cubes
pagenum: 17; label: 2-4
title: Walks, Paths, and Circuits
pagenum: 19; label: 2-5
title: Connected Graphs, Disconnected Graphs, and Components
pagenum: 21; label: 2-6
title: Euler Graphs
pagenum: 23; label: 2-7
title: Operations On Graphs
pagenum: 26; label: 2-8
title: More on Euler Graphs
pagenum: 28; label: 2-9
title: Hamiltonian Paths and Circuits
pagenum: 30; label: 2-10
title: The Traveling Salesman Problem
pagenum: 34; title: Summary
pagenum: 35; title: References
pagenum: 35; title: Problems
pagenum: 36; label: 3
title: Trees and Fundamental Circuits
pagenum: 39; label: 3-1
title: Trees
pagenum: 39; label: 3-2
title: Some Properties of Trees
pagenum: 41; label: 3-3
title: Pendant Vertices in a Tree
pagenum: 43; label: 3-4
title: Distance and Centers in a Tree
pagenum: 45; label: 3-5
title: Rooted and Binary Trees
pagenum: 48; label: 3-6
title: On Counting Trees
pagenum: 52; label: 3-7
title: Spanning Trees
pagenum: 55; label: 3-8
title: Fundamental Circuits
pagenum: 57; label: 3-9
title: Finding All Spanning Trees of a Graph
pagenum: 58; label: 3-10
title: Spanning Trees in a Weighted Graph
pagenum: 61; title: Summary
pagenum: 64; title: References
pagenum: 64; title: Problems
pagenum: 65; label: 4
title: Cut-Sets and Cut-Vertices
pagenum: 68; label: 4-1
title: Cut-Sets
pagenum: 68; label: 4-2
title: Some Properties of a Cut-Set
pagenum: 69; label: 4-3
title: All Cut-Sets in a Graph
pagenum: 71; label: 4-4
title: Fundamental Circuits and Cut-Sets
pagenum: 73; label: 4-5
title: Connectivity and Separability
pagenum: 75; label: 4-6
title: Network Flows
pagenum: 79; label: 4-7
title: 1-Isomorphism
pagenum: 80; label: 4-8
title: 2-Isomorphism
pagenum: 82; title: Summary
pagenum: 85; title: References
pagenum: 86; title: Problems
pagenum: 86; label: 5
title: Planar and Dual Graphs
pagenum: 88; label: 5-1
title: Combinatorial Vs. Geometric Graphs
pagenum: 88; label: 5-2
title: Planar Graphs
pagenum: 90; label: 5-3
title: Kuratowski's Two Graphs
pagenum: 90; label: 5-4
title: Different Representations of a Planar Graph
pagenum: 93; label: 5-5
title: Detection of Planarity
pagenum: 99; label: 5-6
title: Geometric Dual
pagenum: 102; label: 5-7
title: Combinatorial Dual
pagenum: 104; label: 5-8
title: More on Criteria of Planarity
pagenum: 107; label: 5-9
title: Thickness and Crossings
pagenum: 108; title: Summary
pagenum: 109; title: References
pagenum: 110; title: Problems
pagenum: 110; label: 6
title: Vector Spaces of a Graph
pagenum: 112; label: 6-1
title: Sets with One Operation
pagenum: 112; label: 6-2
title: Sets with Two Operations
pagenum: 116; label: 6-3
title: Modular Arithmetic and Galois Fields
pagenum: 118; label: 6-4
title: Vectors and Vector Spaces
pagenum: 120; label: 6-5
title: Vector Space Associated with a Graph
pagenum: 121; label: 6-6
title: Basis Vectors of a Graph
pagenum: 123; label: 6-7
title: Circuit and Cut-Set Subspaces
pagenum: 125; label: 6-8
title: Orthogonal Vectors and Spaces
pagenum: 129; label: 6-9
title: Intersection and Join of W and Ws
pagenum: 131; title: Summary
pagenum: 134; title: References
pagenum: 135; title: Problems
pagenum: 135; label: 7
title: Matrix Representation of Graphs
pagenum: 137; label: 7-1
title: Incidence Matrix
pagenum: 137; label: 7-2
title: Submatrices of A(G)
pagenum: 141; label: 7-3
title: Circuit Matrix
pagenum: 142; label: 7-4
title: Fundamental Circuit Matrix and Rank of B
pagenum: 144; label: 7-5
title: An Application to a Switching Network
pagenum: 146; label: 7-6
title: Cut-Set Matrix
pagenum: 151; label: 7-7
title: Relationships among Af, Bf, and Cf
pagenum: 153; label: 7-8
title: Path Matrix
pagenum: 156; label: 7-9
title: Adjacency Matrix
pagenum: 157; title: Summary
pagenum: 162; title: References
pagenum: 162; title: Problems
pagenum: 162; label: 8
title: Coloring, Covering, and Partitioning
pagenum: 165; label: 8-1
title: Chromatic Number
pagenum: 165; label: 8-2
title: Chromatic Partitioning
pagenum: 169; label: 8-3
title: Chromatic Polynomial
pagenum: 174; label: 8-4
title: Matchings
pagenum: 177; label: 8-5
title: Coverings
pagenum: 182; label: 8-6
title: The Four Color Problem
pagenum: 186; title: Summary
pagenum: 190; title: References
pagenum: 190; title: Problems
pagenum: 192; label: 9
title: Directed Graphs
pagenum: 194; label: 9-1
title: What Is a Directed Graph?
pagenum: 194; label: 9-2
title: Some Types of Digraphs
pagenum: 197; label: 9-3
title: Digraphs and Binary Relations
pagenum: 198; label: 9-4
title: Directed Paths and Connectedness
pagenum: 201; label: 9-5
title: Euler Digraphs
pagenum: 203; label: 9-6
title: Trees with Directed Edges
pagenum: 206; label: 9-7
title: Fundamental Circuits in Digraphs
pagenum: 212; label: 9-8
title: Matrices A, B, and C of Digraphs
pagenum: 213; label: 9-9
title: Adjacency Matrix of a Digraph
pagenum: 220; label: 9-10
title: Paired Comparisons and Tournaments
pagenum: 227; label: 9-11
title: Acyclic Digraphs and Decyclization
pagenum: 230; title: Summary
pagenum: 233; title: References
pagenum: 234; title: Problems
pagenum: 234; label: 10
title: Enumeration of Graphs
pagenum: 238; label: 10-1
title: Types of Enumeration
pagenum: 238; label: 10-2
title: Counting Labeled Trees
pagenum: 240; label: 10-3
title: Counting Unlabeled Trees
pagenum: 241; label: 10-4
title: Polya's Counting Theorem
pagenum: 250; label: 10-5
title: Graph Enumeration With Polya's Theorem
pagenum: 260; title: Summary
pagenum: 264; title: References
pagenum: 264; title: Problems
pagenum: 265; label: 11
title: Graph Theoretic Algorithms and Computer Programs
pagenum: 268; label: 11-1
title: Algorithms
pagenum: 269; label: 11-2
title: Input: Computer Representation of a Graph
pagenum: 270; label: 11-3
title: The Output
pagenum: 273; label: 11-4
title: Some Basic Algorithms
pagenum: 274; label: Algorithm 1
title: Connectedness and Components
pagenum: 274; label: Algorithm 2
title: A Spanning Tree
pagenum: 277; label: Algorithm 3
title: A Set of Fundamental Circuits
pagenum: 280; label: Algorithm 4
title: Cut-Vertices and Separability
pagenum: 284; label: Algorithm 5
title: Directed Circuits
pagenum: 287; label: 11-5
title: Shortest-Path Algorithms
pagenum: 290; label: Algorithm 6
title: Shortest Path from a Specified Vertex to Another Specified Vertex
pagenum: 292; label: Algorithm 7
title: Shortest Path between All Pairs of Vertices
pagenum: 297; label: 11-6
title: Depth-First Search on a Graph
pagenum: 301; label: Algorithm 8
title: Planarity Testing
pagenum: 304; label: 11-7
title: Algorithm 9: Isomorphism
pagenum: 310; label: 11-8
title: Other Graph-Theoretic Algorithms
pagenum: 312; label: 11-9
title: Performance of Graph-Theoretic Algorithms
pagenum: 314; label: 11-10
title: Graph-Theoretic Computer Languages
pagenum: 316; title: Summary
pagenum: 317; title: References
pagenum: 318; title: Problems
pagenum: 321; title: Appendix of Programs
pagenum: 323; label: 12
title: Graphs in Switching and Coding Theory
pagenum: 328; label: 12-1
title: Contact Networks
pagenum: 329; label: 12-2
title: Analysis of Contact Networks
pagenum: 330; label: 12-3
title: Synthesis of Contact Networks
pagenum: 334; label: 12-4
title: Sequential Switching Networks
pagenum: 342; label: 12-5
title: Unit Cube and Its Graph
pagenum: 348; label: 12-6
title: Graphs in Coding Theory
pagenum: 351; title: Summary
pagenum: 351; title: References
pagenum: 354; title: Problems
pagenum: 354; label: 13
title: Electrical Network Analysis by Graph Theory
pagenum: 356; label: 13-1
title: What Is an Electrical Network ?
pagenum: 357; label: 13-2
title: Kirchhoff's Current and Voltage Laws
pagenum: 358; label: 13-3
title: Loop Currents and Node Voltages
pagenum: 359; label: 13-4
title: RLC Networks with Independent Sources: Nodal Analysis
pagenum: 362; label: 13-5
title: RLC Networks with Independent Sources: Loop Analysis
pagenum: 371; label: 13-6
title: General Lumped, Linear; Fixed Networks
pagenum: 373; title: Summary
pagenum: 379; title: References
pagenum: 381; title: Problems
pagenum: 381; label: 14
title: Graph Theory in Operations Research
pagenum: 384; label: 14-1
title: Transport Networks
pagenum: 384; label: 14-2
title: Extensions of Max-Flow Min-Cut Theorem
pagenum: 390; label: 14-3
title: Minimal Cost Flows
pagenum: 393; label: 14-4
title: The Multicommodity Flow
pagenum: 395; label: 14-5
title: Further Applications
pagenum: 396; label: 14-6
title: More on Flow Problems
pagenum: 397; label: 14-7
title: Activity Networks in Project Planning
pagenum: 400; label: 14-8
title: Analysis of an Activity Network
pagenum: 402; label: 14-9
title: Further Comments on Activity Networks
pagenum: 408; label: 14-10
title: Graphs in Game Theory
pagenum: 409; title: Summary
pagenum: 414; title: References
pagenum: 414; label: 15
title: Survey of Other Applications
pagenum: 416; label: 15-1
title: Signal-Flow Graphs
pagenum: 416; label: 15-2
title: Graphs in Markov Processes
pagenum: 424; label: 15-3
title: Graphs in Computer Programming
pagenum: 439; label: 15-4
title: Graphs in Chemistry
pagenum: 449; label: 15-5
title: Miscellaneous Applications
pagenum: 454; label: Appendix A
title: Binet-Cauchy Theorem
pagenum: 458; label: Appendix B
title: Nullity of a Matrix and Sylvester's Law
pagenum: 460; title: Index
pagenum: 463