Book:Gary Chartrand/Introductory Graph Theory

Subject Matter

 * Graph Theory

Republication with corrections of Graphs as Mathematical Models from $1977$.

Contents

 * Preface


 * Acknowledgements


 * Chapter l: Mathematical Models
 * 1.1 Nonmathematical Models
 * 1.2 Mathematical Models
 * 1.3 Graphs
 * 1.4 Graphs as Mathematical Models
 * 1.5 Directed Graphs as Mathematical Models
 * 1.6 Networks as Mathematical Models


 * Chapter 2: Elementary Concepts of Graph Theory
 * 2.1 The Degree of a Vertex
 * 2.2 Isomorphic Graphs
 * 2.3 Connected Graphs
 * 2.4 Cut-Vertices and Bridges


 * Chapter 3: Transportation Problems
 * 3.1 The Königsberg Bridge Problem: An Introduction to Eulerian Graphs
 * 3.2 The Salesman's Problem: An Introduction to Hamiltonian Graphs


 * Chapter 4: Connection Problems
 * 4.1: The Minimal Cohnector Problem: An Introduction to Trees
 * 4.2 Trees and Probability
 * 4.3 PERT and the Critical Path Method


 * Chapter 5: Party Problems
 * 5.1 The Problem of the Eccentric Hosts: An Introduction to Ramsey Numbers
 * 5.2 The Dancing Problem: An Introduction to Matching


 * Chapter 6: Games and Puzzles
 * 6.1 The Problem of the Four Multicolored Cubes: A Solution to "Instant Insanity"
 * 6.2 The Knight's Tour
 * 6.3 The Tower of Hanoi
 * 6.4 The Three Cannibals and Three Missionaries Problem


 * Chapter 7: Digraphs and Mathematical Models
 * 7.1 A Traffic System Problem: An Introduction to Orientable Graphs
 * 7.2 Tournaments
 * 7.3 Paired Comparisons and How to Fix Elections


 * Chapter 8: Graphs and Social Psychology
 * 8.1 The Problem of Balance
 * 8.2 The Problem of Clustering
 * 8.3 Graphs and Transactional Analysis


 * Chapter 9
 * Planar Graphs and Coloring Problems
 * 9.1 The Three Houses and Three Utilities Problem: An Introduction to Planar Graphs
 * 9.2 A Scheduling Problem: An Introduction to Chromatic Numbers
 * 9.3 The Four Color Problem


 * Chapter 10: Graphs and Other Mathematics
 * 10.1 Graphs and Matrices
 * 10.2 Graphs and Topology
 * 10.3 Graphs and Groups


 * Appendix: Sets, Relations, Functions, Proofs
 * A.1 Sets and Subsets
 * A.2 Cartesian Products and Relations
 * A.3 Equivalence Relations
 * A.4 Functions
 * A.5 Theorems and Proofs
 * A.6 Mathematical Induction


 * Answers, Hints, and Solutions to Selected Exercises


 * Index



Source work progress
* : $\S 4.2$: Trees and Probability -- there are gaps. Revisiting as follows:


 * : Chapter $1$: Mathematical Models: $\S 1.5$: Directed Graphs as Mathematical Models


 * Much has been missed out because it discusses applications of an open-ended and imprecisely defined nature.


 * : Appendix $\text{A}.6$: Mathematical Induction: Problem Set $\text{A}.6$: $41$ Complete except for final set of exercises (they go up to $55$) and some simple exercises on logic