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.

From the circuit diagrams of physics and electronics to psychology's sociograms and the communications networks employed by operational research, an extraordinary variety of disciplines rely on graphs to convey fundamentals as well as finer points. With this concise and well-written text, any reader possessing a firm grasp of general mathematics can follow the development of graph theory and learn to apply its principles in methods both formal and abstract.
The first full-length book in English on graph theory, this volume is the work of a distinguished mathematician who has made significant original contributions to the subject. His frequent use of practical examples illustrates the theory's broad range of applications, providing a versatile mathematical technique appropriate to the behavioral sciences, information theory, cybernetics, and other areas, in addition to mathematical disciplines such as set and matrix theory.
The author begins with the simplest theorems, stated in the most general terms possible for economy of thought and exposition. He gradually builds to more complex theorems, expressed in more exacting proofs and reflecting the results of extensive studies. Definitions from algebra and the theory of sets appear at the start and are supplemented as needed.
Students, teachers, and anyone interested in effective communication of research results will find this text a valuable source of instruction.

The ever-expanding field of extremal graph theory encompasses a diverse array of problem-solving methods, including applications to economics, computer science, and optimization theory. This volume, based on a series of lectures delivered to graduate students at the University of Cambridge, presents a concise yet comprehensive treatment of extremal graph theory.
Unlike most graph theory treatises, this text features complete proofs for almost all of its results. Further insights into theory are provided by the numerous exercises of varying degrees of difficulty that accompany each chapter. Although geared toward mathematicians and research students, much of Extremal Graph Theory is accessible even to undergraduate students of mathematics. Pure mathematicians will find this text a valuable resource in terms of its unusually large collection of results and proofs, and professionals in other fields with an interest in the applications of graph theory will also appreciate its precision and scope.

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 well-organized coverage of the fundamentals of graph theory in this highly readable and thoroughly enjoyable book.

Published in 2015, this book not only addresses these issues in a scientific and objective manner but also leads the reader through new search paths. Many books on the theme have been already published, but none of them contains such a large quantity of scientific news and reports.

Increased interest in graph theory in recent years has led to a demand for more textbooks on the subject. With this volume Professor Tutte helps to meet the demand by setting down the sort of information he himself would have found valuable during his research.

The author concentrates here on the general theory of undirected graphs: after some introductory chapters he deals with Euler paths, the symmetry of graphs, the girth or minimum polygon-size, and questions involving non-separability and triple connections. The work is based to a large extent on the papers of Hasslet Whitney on graph theory, published between 1931 and 1935, with the addition of a number of results throught to be new. These include the proof of the uniqueness of the 7-cage, the theory of decomposition of a 2-connection graph into 3-connected clevage units, and the theory of nodal 3-commection.

This volume will be particularly useful to all those interested in graph theory, and especially to those who wish to do research in the field.

Whether you are looking for an introduction to the field of tree balance, a reference work on the multitude of available balance indices or inspiration for your future research, this book offers all three. It delves into the significance of tree balance in phylogenetics and other research domains, where numerous indices have been introduced over the years. While the variations in definitions and underlying principles among these indices have long remained a challenge, this survey addresses the problem by presenting formal definitions of balance and imbalance indices and establishing desirable properties.

The book is comprehensive both in the inclusion of a variety of indices and in the information provided on them: the authors meticulously analyze and categorize established indices, shedding light on their general, statistical and combinatorial properties. They reveal that, while some known balance indices fail to meet the most basic criteria, certain tree shape statistics from other contexts prove to be effective balance measures. The collected properties are neatly presented, numerous new results are established, open research questions are highlighted, and possible applications are discussed.

Reviewing over twenty (im)balance indices, a wealth of mathematical insights is provided, accompanied by real-world examples showcasing the importance of tree balance in diverse research areas. Catering to researchers, students, mathematicians, and biologists, the book can be used as a textbook for university seminars, a reference on tree balance, and as a source of inspiration for future research. It is accompanied by the free R package 'treebalance', a powerful tool to further explore and apply the discussed concepts, and a website allowing quick access to the main information and the latest developments in the field.