Graphical Enumeration

The book is a definitive treatise on the enumeration of graphs and related structural configurations, providing historical results as well as recent developments having potential application in the fields of physics, chemistry, computer science, and electrical engineering. Its ten chapters cover the subjects of labeled enumeration, Polya's Theorem, trees, graphs, diagraphs, power group enumeration, superposition, blocks, asymptotics, and as a special feature, a new comprehensive list of unsolved graphical enumeration problems. It includes an extensive bibliography and numerous exercises ranging in difficulty from routine to intractable. Graphical Enumeration deals with the enumeration of various kinds of graphs. Topics covered range from labeled enumeration and George Pólya's theorem to rooted and unrooted trees, graphs and digraphs, and power group enumeration. Superposition, blocks, and asymptotics are also discussed. A number of unsolved enumeration problems are presented. Comprised of 10 chapters, this book begins with an overview of labeled graphs, followed by a description of the basic enumeration theorem of Pólya. The next three chapters count an enormous variety of trees, graphs, and digraphs. The Power Group Enumeration Theorem is then described together with some of its applications, including the enumeration of self-complementary graphs and digraphs and finite automata. Two other chapters focus on the counting of superposition and blocks, while another chapter is devoted to asymptotic numbers that are developed for several different graphical structures. The book concludes with a comprehensive definitive list of unsolved graphical enumeration problems. This monograph will be of interest to both students and practitioners of mathematics. Content: Front Matter, Page iii Copyright, Page iv Dedication, Page v PREFACE, Pages xi-xiv Chapter 1 - LABELED ENUMERATION, Pages 1-31 Chapter 2 - PÓLYA'S THEOREM, Pages 32-50 Chapter 3 - TREES, Pages 51-80 Chapter 4 - GRAPHS, Pages 81-118 Chapter 5 - DIGRAPHS, Pages 119-134 Chapter 6 - POWER GROUP ENUMERATION, Pages 135-157 Chapter 7 - SUPERPOSITION, Pages 158-176 Chapter 8 - BLOCKS, Pages 177-194 Chapter 9 - ASYMPTOTICS, Pages 195-215 Chapter 10 - UNSOLVED PROBLEMS, Pages 216-237 Appendix I, Pages 239-246 Appendix II, Pages 247-248 Appendix III, Pages 249-252 BIBLIOGRAPHY, Pages 253-261 INDEX OF SYMBOLS, Pages 263-265 INDEX OF DEFINITIONS, Pages 267-271 [by] Frank Harary [and] Edgar M. Palmer. Bibliography: P. 253-261.