Book:Gary Chartrand/Introductory Graph Theory

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Gary Chartrand: Introductory Graph Theory

Published $1985$, Dover Publications, Inc.

ISBN 0-486-24775-9.


Subject Matter

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