The history, formulas, and most famous puzzles of graph theory Graph theory goes back several centuries and revolves around the study of graphs—mathematical structures showing relations between objects. With applications in biology, computer science, transportation science, and other areas, graph theory encompasses some of the most beautiful formulas in mathematics—and some of its most famous problems. The Fascinating World of Graph Theory explores the questions and puzzles that have been studied, and often solved, through graph theory. This book looks at graph theory's development and the vibrant individuals responsible for the field's growth. Introducing fundamental concepts, the authors explore a diverse plethora of classic problems such as the Lights Out Puzzle, and each chapter contains math exercises for readers to savor. An eye-opening journey into the world of graphs, The Fascinating World of Graph Theory offers exciting problem-solving possibilities for mathematics and beyond.

Cutting-edge coverage of graph theory and geography in a high-tech, user-friendly format Available only as a highly interactive e-book, this revolutionary volume allows mathematicians and geographers to view graph theory in a new and vibrant way. Renowned experts in the field, the authors provide complete, up-to-date coverage of relevant theories using real-world examples to highlight the synthetic nature of graph theory and geography and help professionals and students find new, concrete applications. Theories and definitions are accompanied by complementary chapters that explain the mathematics behind the examples and provide quick reference options. Brilliant, four-color graphics elucidate this comprehensive treatment, while the e-book format allows for uncommon flexibility and ease of use. The electronic format takes full advantage of online tools such as animation and Java; applets to allow readers to follow processes as they happen, while hyperlinks allow readers to move easily through the text for quick reference to theorems or definitions. Available with a free, enhanced e-book reader, Graph Theory and Geography offers comprehensive coverage and unprecedented convenience to readers at almost any level of experience.

From specialists in the field, you will learn about interesting connections and recent developments in the field of graph theory by looking in particular at Cartesian products-arguably the most important of the four standard graph products. Many new results in this area appear for the first time in print in this book. Written in an accessible way,

Graphs & Digraphs masterfully employs student-friendly exposition, clear proofs, abundant examples, and numerous exercises to provide an essential understanding of the concepts, theorems, history, and applications of graph theory. Fully updated and thoughtfully reorganized to make reading and locating material easier for instructors and students, the Sixth Edition of this bestselling, classroom-tested text: Adds more than 160 new exercises Presents many new concepts, theorems, and examples Includes recent major contributions to long-standing conjectures such as the Hamiltonian Factorization Conjecture, 1-Factorization Conjecture, and Alspach's Conjecture on graph decompositions Supplies a proof of the perfect graph theorem Features a revised chapter on the probabilistic method in graph theory with many results integrated throughout the text At the end of the book are indices and lists of mathematicians' names, terms, symbols, and useful references. There is also a section giving hints and solutions to all odd-numbered exercises. A complete solutions manual is available with qualifying course adoption. Graphs & Digraphs, Sixth Edition remains the consummate text for an advanced undergraduate level or introductory graduate level course or two-semester sequence on graph theory, exploring the subject's fascinating history while covering a host of interesting problems and diverse applications.

Now in a new, revised edition, this book provides readers with an introduction to graph theory. The authors enhance the basic material by including a wide variety of applications to both other branches of mathematics and to real-world problems. Each application has been carefully selected and is treated in some depth. Also emphasized throughout the book is the importance of efficient methods of solving problems.