This comprehensive text offers undergraduates a remarkably student-friendly introduction to graph theory. Written by two of the field's most prominent experts, it takes an engaging approach that emphasizes graph theory's history. Unique examples and lucid proofs provide a sound yet accessible treatment that stimulates interest in an evolving subject and its many applications.Optional sections designated as "excursion" and "exploration" present interesting sidelights of graph theory and touch upon topics that allow students the opportunity to experiment and use their imaginations. Three appendixes review important facts about sets and logic, equivalence relations and functions, and the methods of proof. The text concludes with solutions or hints for odd-numbered exercises, in addition to references, indexes, and a list of symbols.

The primary aim of this book is to present a coherent introduction to graph theory, suitable as a textbook for advanced undergraduate and beginning graduate students in mathematics and computer science. It provides a systematic treatment of the theory of graphs without sacrificing its intuitive and aesthetic appeal. Commonly used proof techniques are described and illustrated. The book also serves as an introduction to research in graph theory.

This book aims to explain the basics of graph theory that are needed at an introductory level for students in computer or information sciences. To motivate students and to show that even these basic notions can be extremely useful, the book also aims to provide an introduction to the modern field of network science.Mathematics is often unnecessarily difficult for students, at times even intimidating. For this reason, explicit attention is paid in the first chapters to mathematical notations and proof techniques, emphasizing that the notations form the biggest obstacle, not the mathematical concepts themselves. This approach allows to gradually prepare students for using tools that are necessary to put graph theory to work: complex networks.In the second part of the book the student learns about random networks, small worlds, the structure of the Internet and the Web, peer-to-peer systems, and social networks. Again, everything is discussed at an elementary level, but such that in the end students indeed have the feeling that they:1.Have learned how to read and understand the basic mathematics related to graph theory.2.Understand how basic graph theory can be applied to optimization problems such as routing in communication networks.3.Know a bit more about this sometimes mystical field of small worlds and random networks.There is an accompanying web site www.distributed-systems.net/gtcn from where supplementary material can be obtained, including exercises, Mathematica notebooks, data for analyzing graphs, and generators for various complex networks.

Alexander, Christopher. The Timeless Way of Building. New York, Oxford University Press, 1979. 20 cm x 13,8 cm. XV, 552 pages. With several black-and-white illustrations throughout book. Original Hardcover. Very good condition with only minor signs of external wear. Only slightly foxed. Includes for example the following essays: Patterns which are alive / The multiplicity of living patterns / Our pattern languages / The creative power of language / The breakdown of language / The structure of language / The evolution of a common language / The genetic power of language / The process of construction / The slow emergence of a town / The kernel of the way etc etc. Christopher Wolfgang Alexander (born October 4, 1936 in Vienna, Austria) is an architect noted for his theories about design as well as over 200 building projects around the world. Reasoning that users know more about the buildings they need than any architect could, he produced and validated (in collaboration with Sarah Ishikawa and Murray Silverstein) a pattern language to empower anyone to design and build at any scale. He moved from England to the United States in 1958, living and teaching in Berkeley, California from 1963. Currently an emeritus professor at the University of California, Berkeley, Alexander lives in Arundel, England. Alexander is often overlooked by texts in the history and theory of architecture because his work intentionally disregards contemporary architectural discourse. However, Alexander's polyvalent approach to the discipline of architecture has had enormous ramifications through his vast corpus of essays and books. He is regarded as the father of the Pattern Language movement, and various contemporary architectural practices such as the New Urbanist movement have resulted from Alexander's ideas, which seek to help normal people reclaim control over their built environments. (Wikipedia).

Networks are everywhere, from the internet, to social networks, and the genetic networks that determine our biological existence. Illustrated throughout in full colour, this pioneering textbook, spanning a wide range of topics from physics to computer science, engineering, economics and the social sciences, introduces network science to an interdisciplinary audience. From the origins of the six degrees of separation to explaining why networks are robust to random failures, the author explores how viruses like Ebola and H1N1 spread, and why it is that our friends have more friends than we do. Using numerous real-world examples, this innovatively designed text includes clear delineation between undergraduate and graduate level material. The mathematical formulas and derivations are included within Advanced Topics sections, enabling use at a range of levels. Extensive online resources, including films and software for network analysis, make this a multifaceted companion for anyone with an interest in network science.

This newly expanded and updated second edition of the best-selling classic continues to take the "mystery" out of designing algorithms, and analyzing their efficacy and efficiency. Expanding on the first edition, the book now serves as the primary textbook of choice for algorithm design courses while maintaining its status as the premier practical reference guide to algorithms for programmers, researchers, and students.The reader-friendly Algorithm Design Manual provides straightforward access to combinatorial algorithms technology, stressing design over analysis. The first part, Techniques, provides accessible instruction on methods for designing and analyzing computer algorithms. The second part, Resources, is intended for browsing and reference, and comprises the catalog of algorithmic resources, implementations and an extensive bibliography.NEW to the second edition:• Doubles the tutorial material and exercises over the first edition\n• Provides full online support for lecturers, and a completely updated and improved website component with lecture slides, audio and video• Contains a unique catalog identifying the 75 algorithmic problems that arise most often in practice, leading the reader down the right path to solve them• Includes several NEW "war stories" relating experiences from real-world applications\n• Provides up-to-date links leading to the very best algorithm implementations available in C, C++, and Java

For undergraduate or graduate courses in Graph Theory in departments of mathematics or computer science. This title is part of the Pearson Modern Classics series. Pearson Modern Classics are acclaimed titles at a value price. Please visit www.pearsonhighered.com/math-classics-series for a complete list of titles. This text offers a comprehensive and coherent introduction to the fundamental topics of graph theory. It includes basic algorithms and emphasizes the understanding and writing of proofs about graphs. Thought-provoking examples and exercises develop a thorough understanding of the structure of graphs and the techniques used to analyze problems. The first seven chapters form the basic course, with advanced material in Chapter 8.

Already an international bestseller, with the release of this greatly enhanced second edition, Graph Theory and Its Applications is now an even better choice as a textbook for a variety of courses -- a textbook that will continue to serve your students as a reference for years to come.The superior explanations, broad coverage, and abundance of illustrations and exercises that positioned this as the premier graph theory text remain, but are now augmented by a broad range of improvements. Nearly 200 pages have been added for this edition, including nine new sections and hundreds of new exercises, mostly non-routine. What else is new?\nNew chapters on measurement and analytic graph theory \n\nSupplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing.\n\nSolutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth\n\nReorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition\n\nForeshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of readerGross and Yellen take a comprehensive approach to graph theory that integrates careful exposition of classical developments with emerging methods, models, and practical needs. Their unparalleled treatment provides a text ideal for a two-semester course and a variety of one-semester classes, from an introductory one-semester course to courses slanted toward classical graph theory, operations research, data structures and algorithms, or algebra and topology.

An in-depth account of graph theory, written for serious students of mathematics and computer science. It reflects the current state of the subject and emphasises connections with other branches of pure mathematics. Recognising that graph theory is one of several courses competing for the attention of a student, the book contains extensive descriptive passages designed to convey the flavour of the subject and to arouse interest. In addition to a modern treatment of the classical areas of graph theory, the book presents a detailed account of newer topics, including Szemerédis Regularity Lemma and its use, Shelahs extension of the Hales-Jewett Theorem, the precise nature of the phase transition in a random graph process, the connection between electrical networks and random walks on graphs, and the Tutte polynomial and its cousins in knot theory. Moreover, the book contains over 600 well thought-out exercises: although some are straightforward, most are substantial, and some will stretch even the most able reader.

"Innovative introductory text . . . clear exposition of unusual and more advanced topics . . . Develops material to substantial level." — American Mathematical Monthly"Refreshingly different . . . an ideal training ground for the mathematical process of investigation, generalization, and conjecture leading to the discovery of proofs and counterexamples." — American Mathematical Monthly" . . . An excellent textbook for an undergraduate course." — Australian Computer JournalA stimulating view of mathematics that appeals to students as well as teachers, this undergraduate-level text is written in an informal style that does not sacrifice depth or challenge. Based on 20 years of teaching by the leading researcher in graph theory, it offers a solid foundation on the subject. This revised and augmented edition features new exercises, simplifications, and other improvements suggested by classroom users and reviewers. Topics include 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.

Provides a basic foundation on trees, algorithms, Eulerian and Hamilton graphs, planar graphs and coloring, with special reference to four color theorem. Discusses directed graphs and transversal theory and related these areas to Markov chains and network flows. Paper.

Defines and explores the implementation and figures of the algorithms required for various applications, offering commentary, descriptions, and exercises for developers, researchers, and students.

This is a textbook for an introductory combinatorics course lasting one or two semesters. An extensive list of problems, ranging from routine exercises to research questions, is included. In each section, there are also exercises that contain material not explicitly discussed in the preceding text, so as to provide instructors with extra choices if they want to shift the emphasis of their course. Just as with the first two editions, the new edition walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some recent progress in the area: on the one hand, providing material that will help students learn the basic techniques, and on the other hand, showing that some questions at the forefront of research are comprehensible and accessible to the talented and hardworking undergraduate. The basic topics discussed are: the twelvefold way, cycles in permutations, the formula of inclusion and exclusion, the notion of graphs and trees, matchings, Eulerian and Hamiltonian cycles, and planar graphs. The selected advanced topics are: Ramsey theory, pattern avoidance, the probabilistic method, partially ordered sets, the theory of designs (new to this edition), enumeration under group action (new to this edition), generating functions of labeled and unlabeled structures and algorithms and complexity. As the goal of the book is to encourage students to learn more combinatorics, every effort has been made to provide them with a not only useful, but also enjoyable and engaging reading.

A comprehensive introduction to network flows that brings together the classic and the contemporary aspects of the field, and provides an integrative view of theory, algorithms, and applications. presents in-depth, self-contained treatments of shortest path, maximum flow, and minimum cost flow problems, including descriptions of polynomial-time algorithms for these core models. \nemphasizes powerful algorithmic strategies and analysis tools such as data scaling, geometric improvement arguments, and potential function arguments. \n\nprovides an easy-to-understand descriptions of several important data structures, including d-heaps, Fibonacci heaps, and dynamic trees. \n\ndevotes a special chapter to conducting empirical testing of algorithms. \n\nfeatures over 150 applications of network flows to a variety of engineering, management, and scientific domains. \n\ncontains extensive reference notes and illustrations.

The scientific study of networks, including computer networks, social networks, and biological networks, has received an enormous amount of interest in the last few years. The rise of the Internet and the wide availability of inexpensive computers have made it possible to gather and analyze network data on a large scale, and the development of a variety of new theoretical tools has allowed us to extract new knowledge from many different kinds of networks.The study of networks is broadly interdisciplinary and important developments have occurred in many fields, including mathematics, physics, computer and information sciences, biology, and the social sciences. This book brings together for the first time the most important breakthroughs in each of these fields and presents them in a coherent fashion, highlighting the strong interconnections between work in different areas. Subjects covered include the measurement and structure of networks in many branches of science, methods for analyzing network data, including methods developed in physics, statistics, and sociology, the fundamentals of graph theory, computer algorithms, and spectral methods, mathematical models of networks, including random graph models and generative models, and theories of dynamical processes taking place on networks.To request a copy of the Solutions Manual, visit: http://global.oup.com/uk/academic/physics/admin/solutions

The history, formulas, and most famous puzzles of graph theory\nGraph 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.