Introductory Graph Theory by Gary Chartrand (English) Paperback Book

Description: Introductory Graph Theory by Gary Chartrand 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. FORMAT Paperback LANGUAGE English CONDITION Brand New Publisher Description 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 colouring 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 well-organised coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book. Author Biography Six 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 (1913-1996), 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 Erdoss 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 worlds active mathematicians have an Erdos number lower than 8. Its somewhat similar to the well-known Hollywood trivia game, Six Degrees of Kevin Bacon. In fact there are some crossovers: Actress-mathematician Danica McKellar, who appeared in TVs 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 Dovers Introductory Graph Theory, has an Erdos number of 1 - and is one of many Dover authors who share this honor. Table of Contents 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 Salesmans 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 Knights 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 Long Description 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. Details ISBN0486247759 Author Gary Chartrand Pages 320 Language English ISBN-10 0486247759 ISBN-13 9780486247755 Media Book Format Paperback DEWEY 511.5 Abridged Yes Imprint Dover Publications Inc. Place of Publication New York Country of Publication United States Illustrations illustrations Short Title INTRODUCTORY GRAPH THEORY DOI 10.1604/9780486247755 UK Release Date 2003-03-28 AU Release Date 2003-03-28 NZ Release Date 2003-03-28 US Release Date 2003-03-28 Publisher Dover Publications Inc. Edition Description Abridged edition Year 2003 Publication Date 2003-03-28 Audience General Series Dover Books on Mathema 1.4tics We've got this At The Nile, if you're looking for it, we've got it. With fast shipping, low prices, friendly service and well over a million items - you're bound to find what you want, at a price you'll love! TheNile_Item_ID:7596090;

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