Introductory Graph Theory

Chapter 1 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 Konigsberg 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 Connector 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 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