Graph theory with applications to engineering and computer science. - Info and Reading Options

"Graph theory with applications to engineering and computer science." Table Of Contents:

• 1- Preface
• 2- Introduction
• 3- What is a Graph?
• 4- Application of Graphs
• 5- Finite and Infinite Graphs
• 6- Incidence and Degree
• 7- Isolated Vertex, Pendant Vertex, and Null Graph
• 8- Brief History of Graph Theory
• 9- Summary
• 10- References
• 11- Problems
• 12- Paths and Circuits
• 13- Isomorphism
• 14- Subgraphs
• 15- A Puzzle With Multicolored Cubes
• 16- Walks, Paths, and Circuits
• 17- Connected Graphs, Disconnected Graphs, and Components
• 18- Euler Graphs
• 19- Operations On Graphs
• 20- More on Euler Graphs
• 21- Hamiltonian Paths and Circuits
• 22- The Traveling Salesman Problem
• 23- Summary
• 24- References
• 25- Problems
• 26- Trees and Fundamental Circuits
• 27- Trees
• 28- Some Properties of Trees
• 29- Pendant Vertices in a Tree
• 30- Distance and Centers in a Tree
• 31- Rooted and Binary Trees
• 32- On Counting Trees
• 33- Spanning Trees
• 34- Fundamental Circuits
• 35- Finding All Spanning Trees of a Graph
• 36- Spanning Trees in a Weighted Graph
• 37- Summary
• 38- References
• 39- Problems
• 40- Cut-Sets and Cut-Vertices
• 41- Cut-Sets
• 42- Some Properties of a Cut-Set
• 43- All Cut-Sets in a Graph
• 44- Fundamental Circuits and Cut-Sets
• 45- Connectivity and Separability
• 46- Network Flows
• 47- 1-Isomorphism
• 48- 2-Isomorphism
• 49- Summary
• 50- References
• 51- Problems
• 52- Planar and Dual Graphs
• 53- Combinatorial Vs. Geometric Graphs
• 54- Planar Graphs
• 55- Kuratowski's Two Graphs
• 56- Different Representations of a Planar Graph
• 57- Detection of Planarity
• 58- Geometric Dual
• 59- Combinatorial Dual
• 60- More on Criteria of Planarity
• 61- Thickness and Crossings
• 62- Summary
• 63- References
• 64- Problems
• 65- Vector Spaces of a Graph
• 66- Sets with One Operation
• 67- Sets with Two Operations
• 68- Modular Arithmetic and Galois Fields
• 69- Vectors and Vector Spaces
• 70- Vector Space Associated with a Graph
• 71- Basis Vectors of a Graph
• 72- Circuit and Cut-Set Subspaces
• 73- Orthogonal Vectors and Spaces
• 74- Intersection and Join of W and Ws
• 75- Summary
• 76- References
• 77- Problems
• 78- Matrix Representation of Graphs
• 79- Incidence Matrix
• 80- Submatrices of A(G)
• 81- Circuit Matrix
• 82- Fundamental Circuit Matrix and Rank of B
• 83- An Application to a Switching Network
• 84- Cut-Set Matrix
• 85- Relationships among Af, Bf, and Cf
• 86- Path Matrix
• 87- Adjacency Matrix
• 88- Summary
• 89- References
• 90- Problems
• 91- Coloring, Covering, and Partitioning
• 92- Chromatic Number
• 93- Chromatic Partitioning
• 94- Chromatic Polynomial
• 95- Matchings
• 96- Coverings
• 97- The Four Color Problem
• 98- Summary
• 99- References
• 100- Problems
• 101- Directed Graphs
• 102- What Is a Directed Graph?
• 103- Some Types of Digraphs
• 104- Digraphs and Binary Relations
• 105- Directed Paths and Connectedness
• 106- Euler Digraphs
• 107- Trees with Directed Edges
• 108- Fundamental Circuits in Digraphs
• 109- Matrices A, B, and C of Digraphs
• 110- Adjacency Matrix of a Digraph
• 111- Paired Comparisons and Tournaments
• 112- Acyclic Digraphs and Decyclization
• 113- Summary
• 114- References
• 115- Problems
• 116- Enumeration of Graphs
• 117- Types of Enumeration
• 118- Counting Labeled Trees
• 119- Counting Unlabeled Trees
• 120- Polya's Counting Theorem
• 121- Graph Enumeration With Polya's Theorem
• 122- Summary
• 123- References
• 124- Problems
• 125- Graph Theoretic Algorithms and Computer Programs
• 126- Algorithms
• 127- Input: Computer Representation of a Graph
• 128- The Output
• 129- Some Basic Algorithms
• 130- Connectedness and Components
• 131- A Spanning Tree
• 132- A Set of Fundamental Circuits
• 133- Cut-Vertices and Separability
• 134- Directed Circuits
• 135- Shortest-Path Algorithms
• 136- Shortest Path from a Specified Vertex to Another Specified Vertex
• 137- Shortest Path between All Pairs of Vertices
• 138- Depth-First Search on a Graph
• 139- Planarity Testing
• 140- Algorithm 9: Isomorphism
• 141- Other Graph-Theoretic Algorithms
• 142- Performance of Graph-Theoretic Algorithms
• 143- Graph-Theoretic Computer Languages
• 144- Summary
• 145- References
• 146- Problems
• 147- Appendix of Programs
• 148- Graphs in Switching and Coding Theory
• 149- Contact Networks
• 150- Analysis of Contact Networks
• 151- Synthesis of Contact Networks
• 152- Sequential Switching Networks
• 153- Unit Cube and Its Graph
• 154- Graphs in Coding Theory
• 155- Summary
• 156- References
• 157- Problems
• 158- Electrical Network Analysis by Graph Theory
• 159- What Is an Electrical Network ?
• 160- Kirchhoff's Current and Voltage Laws
• 161- Loop Currents and Node Voltages
• 162- RLC Networks with Independent Sources: Nodal Analysis
• 163- RLC Networks with Independent Sources: Loop Analysis
• 164- General Lumped, Linear; Fixed Networks
• 165- Summary
• 166- References
• 167- Problems
• 168- Graph Theory in Operations Research
• 169- Transport Networks
• 170- Extensions of Max-Flow Min-Cut Theorem
• 171- Minimal Cost Flows
• 172- The Multicommodity Flow
• 173- Further Applications
• 174- More on Flow Problems
• 175- Activity Networks in Project Planning
• 176- Analysis of an Activity Network
• 177- Further Comments on Activity Networks
• 178- Graphs in Game Theory
• 179- Summary
• 180- References
• 181- Survey of Other Applications
• 182- Signal-Flow Graphs
• 183- Graphs in Markov Processes
• 184- Graphs in Computer Programming
• 185- Graphs in Chemistry
• 186- Miscellaneous Applications
• 187- Binet-Cauchy Theorem
• 188- Nullity of a Matrix and Sylvester's Law
• 189- Index

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