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Introductory Graph Theoryby Gary Chartrand
Synopses & ReviewsPublisher Comments:Graph theory is used today in the physical sciences, social sciences, computer science, and other areas. Introductory Graph Theory presents a nontechnical introduction to this exciting field in a clear, lively, and informative style. Author Gary Chartrand covers the important elementary topics of graph theory and its applications. In addition, he presents a large variety of proofs designed to strengthen mathematical techniques and offers challenging opportunities to have fun with mathematics. Ten major topics — profusely illustrated — include: Mathematical Models, Elementary Concepts of Graph Theory, Transportation Problems, Connection Problems, Party Problems, Digraphs and Mathematical Models, Games and Puzzles, Graphs and Social Psychology, Planar Graphs and Coloring Problems, and Graphs and Other Mathematics. A useful Appendix covers Sets, Relations, Functions, and Proofs, and a section devoted to exercises — with answers, hints, and solutions — is especially valuable to anyone encountering graph theory for the first time. Undergraduate mathematics students at every level, puzzlists, and mathematical hobbyists will find wellorganized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book. Synopsis:Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more. Synopsis:Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more. Synopsis:Clear, lively style covers all basics of theory and application, including mathematical models, elementary concepts of graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, graphs and social psychology, planar graphs and coloring problems, and graphs and other mathematics. Description:Includes bibliographies and index.
About the AuthorSix Degrees of Paul Erdos Contrary to popular belief, mathematicians do quite often have fun. Take, for example, the phenomenon of the Erdos number. Paul Erdos (19131996), a prominent and productive Hungarian mathematician who traveled the world collaborating with other mathematicians on his research papers. Ultimately, Erdos published about 1,400 papers, by far the most published by any individual mathematician. About 1970, a group of Erdos's friends and collaborators created the concept of the "Erdos number" to define the "collaborative distance" between Erdos and other mathematicians. Erdos himself was assigned an Erdos number of 0. A mathematician who collaborated directly with Erdos himself on a paper (there are 511 such individuals) has an Erdos number of 1. A mathematician who collaborated with one of those 511 mathematicians would have an Erdos number of 2, and so on — there are several thousand mathematicians with a 2. From this humble beginning, the mathematical elaboration of the Erdos number quickly became more and more elaborate, involving mean Erdos numbers, finite Erdos numbers, and others. In all, it is believed that about 200,000 mathematicians have an assigned Erdos number now, and 90 percent of the world's active mathematicians have an Erdos number lower than 8. It's somewhat similar to the wellknown Hollywood trivia game, Six Degrees of Kevin Bacon. In fact there are some crossovers: Actressmathematician Danica McKellar, who appeared in TV's The Wonder Years, has an Erdos number of 4 and a Bacon number of 2. This is all leading up to the fact that Gary Chartrand, author of Dover's Introductory Graph Theory, has an Erdos number of 1 — and is one of many Dover authors who share this honor. Table of ContentsChapter 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 CutVertices 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 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 What Our Readers Are SayingBe the first to add a comment for a chance to win!Product Details
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