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 colo... read more
Topological Graph Theory by Jonathan L. Gross, Thomas W. Tucker Introductory treatment emphasizes graph imbedding but also covers connections between topological graph theory and other areas of mathematics. Discusses role of voltage graphs, Ringel-Youngs theorem, genus of a group, more. 1987 edition.
Introduction to Graph Theory by Richard J. Trudeau Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Introductory Discrete Mathematics by V. K . Balakrishnan This concise, undergraduate-level text focuses on combinatorics, graph theory with applications to some standard network optimization problems, and algorithms. More than 200 exercises, many with complete solutions. 1991 edition.
Matroid Theory by D. J. A. Welsh Text by a noted expert describes standard examples and investigation results, using elementary proofs to develop basic matroid properties before advancing to a more sophisticated treatment. Includes numerous exercises. 1976 edition.
Planar Graphs: Theory and Algorithms by T. Nishizeki, N. Chiba This text features most of the important theorems and algorithms for planar graphs. Suitable as a textbook, it is also useful for researchers and includes an extensive reference section. 1988 edition.
Extremal Graph Theory by Bela Bollobas Concise yet comprehensive, this treatment of extremal graph theory is appropriate for undergraduate and graduate students and features numerous exercises and complete proofs. 1978 edition.
Pearls in Graph Theory: A Comprehensive Introduction by Nora Hartsfield, Gerhard Ringel Stimulating and accessible, this undergraduate-level text covers basic graph theory, colorings of graphs, circuits and cycles, labeling graphs, drawings of graphs, measurements of closeness to planarity, graphs on surfaces, and applications and algorithms. 1994 edition.
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.
Reprint of Graphs as Mathematical Models, Prindle, Weber & Schmidt, Inc., Boston, 1977.
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 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 well-known Hollywood trivia game, Six Degrees of Kevin Bacon. In fact there are some crossovers: Actress-mathematician 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.
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