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Graph Theory, 1736-1936
First published in 1976, this book has been widely acclaimed both for its significant contribution to the history of mathematics and for the way that it brings the subject alive. Building on a set of original writings from some of the founders of graph theory, the book traces the historical development of the subject through a linking commentary. The relevant underlying mathematics is also explained, providing an original introduction to the subject for students. From reviews: 'The book...serves as an excellent examplein fact, as a modelof a new approach to one aspect of mathematics, when mathematics is considered as a living, vital and developing tradition.' (Edward A. Maziark in Isis) 'Big...
A Beginner's Guide to Graph Theory
Graph theory continues to be one of the fastest growing areas of modern mathematics because of its wide applicability in such diverse disciplines as computer science, engineering, chemistry, management science, social science, and resource planning. Graphs arise as mathematical models in these fields, and the theory of graphs provides a spectrum of methods of proof. This concisely written textbook is intended for an introductory course in graph theory for undergraduate mathematics majors or advanced undergraduate and graduate students from the many fields that benefit from graph-theoretic applications. This second edition includes new chapters on labeling and communications networks and smal...
Graph Theory
From the reviews: "Béla Bollobás introductory course on graph theory deserves to be considered as a watershed in the development of this theory as a serious academic subject. ... The book has chapters on electrical networks, flows, connectivity and matchings, extremal problems, colouring, Ramsey theory, random graphs, and graphs and groups. Each chapter starts at a measured and gentle pace. Classical results are proved and new insight is provided, with the examples at the end of each chapter fully supplementing the text... Even so this allows an introduction not only to some of the deeper results but, more vitally, provides outlines of, and firm insights into, their proofs. Thus in an elementary text book, we gain an overall understanding of well-known standard results, and yet at the same time constant hints of, and guidelines into, the higher levels of the subject. It is this aspect of the book which should guarantee it a permanent place in the literature." #Bulletin of the London Mathematical Society#1
Graph Theory
Designed for the non-specialist, this classic text by a world expert is an invaluable reference tool for those interested in a basic understanding of the subject. Exercises, notes and exhaustive references follow each chapter, making it outstanding both as a text and reference for students and researchers in graph theory and its applications.The author approaches the subject with a lively writing style. The reader will delight to discover that the topics in this book are coherently unified and include some of the deepest and most beautiful developments in graph theory.
Graph Theory
Graph Theory presents a natural, reader-friendly way to learn some of the essential ideas of graph theory starting from first principles. The format is similar to the companion text, Combinatorics: A Problem Oriented Approach also by Daniel A. Marcus, in that it combines the features of a textbook with those of a problem workbook. The material is presented through a series of approximately 360 strategically placed problems with connecting text. This is supplemented by 280 additional problems that are intended to be used as homework assignments. Concepts of graph theory are introduced, developed, and reinforced by working through leading questions posed in the problems. This problem-oriented ...
Graph Theory with Applications
Over 1500 problems are used to illustrate concepts, related to different topics, and introduce applications.Over 1000 exercises in the text with many different types of questions posed. Precise mathematical language is used without excessive formalism and abstraction. Care has been taken to balance the mix of notation and words in mathematical statements. Problem sets are stated clearly and unambiguously, and all are carefully graded for various levels of difficulty. This text has been carefully designed for flexible use.
Graph Theory As I Have Known It
A unique introduction to graph theory, written by one of the founding fathers. Professor William Tutte, codebreaker and mathematician, details his experiences in the area and provides a fascinating insight into the processes leading to his proofs.
Graph Theory and Its Engineering Applications
The intuitive diagrammatic nature of graphs makes them useful in modelling systems in engineering problems. This text gives an account of material related to such applications, including minimal cost flows and rectangular dissection and layouts. A major th
The Fascinating World of Graph Theory
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.
A First Course in Graph Theory and Combinatorics
This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
