The Fascinating World Of Graph Theory

Author : Arthur Benjamin,Gary Chartrand,Ping Zhang
Publisher : Princeton University Press
Page : 338 pages
File Size : 45,8 Mb
Release : 2017-06-06
Category : Mathematics
ISBN : 9780691175638

Get Book

The Fascinating World of Graph Theory by Arthur Benjamin,Gary Chartrand,Ping Zhang Pdf

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.

Author : Gary Chartrand,Ping Zhang
Publisher : Courier Corporation
Page : 464 pages
File Size : 55,9 Mb
Release : 2013-05-20
Category : Mathematics
ISBN : 9780486297309

Get Book

A First Course in Graph Theory by Gary Chartrand,Ping Zhang Pdf

Written by two prominent figures in the field, this comprehensive text provides a remarkably student-friendly approach. Its sound yet accessible treatment emphasizes the history of graph theory and offers unique examples and lucid proofs. 2004 edition.

Author : Nora Hartsfield,Gerhard Ringel
Publisher : Courier Corporation
Page : 272 pages
File Size : 45,8 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486315522

Get Book

Pearls in Graph Theory by Nora Hartsfield,Gerhard Ringel Pdf

Stimulating and accessible, this undergraduate-level text covers 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.

Author : Arthur Benjamin
Publisher : Unknown
Page : 332 pages
File Size : 51,6 Mb
Release : 2024-06-02
Category : Electronic
ISBN : 1400897777

Get Book

Fascinating World of Graph Theory (eGalley). by Arthur Benjamin Pdf

Author : W. T. Tutte
Publisher : Clarendon Press
Page : 164 pages
File Size : 55,6 Mb
Release : 2012-05-24
Category : Mathematics
ISBN : 9780191637780

Get Book

Graph Theory As I Have Known It by W. T. Tutte Pdf

This book provides a unique and unusual introduction to graph theory by one of the founding fathers, and will be of interest to all researchers in the subject. It is not intended as a comprehensive treatise, but rather as an account of those parts of the theory that have been of special interest to the author. Professor Tutte details his experience in the area, and provides a fascinating insight into how he was led to his theorems and the proofs he used. As well as being of historical interest it provides a useful starting point for research, with references to further suggested books as well as the original papers. The book starts by detailing the first problems worked on by Professor Tutte and his colleagues during his days as an undergraduate member of the Trinity Mathematical Society in Cambridge. It covers subjects such as comnbinatorial problems in chess, the algebraicization of graph theory, reconstruction of graphs, and the chromatic eigenvalues. In each case fascinating historical and biographical information about the author's research is provided.

Author : Gary Chartrand,Ping Zhang
Publisher : McGraw-Hill Science, Engineering & Mathematics
Page : 0 pages
File Size : 49,7 Mb
Release : 2005
Category : Graph theory
ISBN : 0072948620

Get Book

Introduction to Graph Theory by Gary Chartrand,Ping Zhang Pdf

Economic applications of graphs ands equations, differnetiation rules for exponentiation of exponentials ...

Author : Gary Chartrand,Ping Zhang
Publisher : CRC Press
Page : 503 pages
File Size : 55,8 Mb
Release : 2019-11-28
Category : Mathematics
ISBN : 9780429798283

Get Book

Chromatic Graph Theory by Gary Chartrand,Ping Zhang Pdf

With Chromatic Graph Theory, Second Edition, the authors present various fundamentals of graph theory that lie outside of graph colorings, including basic terminology and results, trees and connectivity, Eulerian and Hamiltonian graphs, matchings and factorizations, and graph embeddings. Readers will see that the authors accomplished the primary goal of this textbook, which is to introduce graph theory with a coloring theme and to look at graph colorings in various ways. The textbook also covers vertex colorings and bounds for the chromatic number, vertex colorings of graphs embedded on surfaces, and a variety of restricted vertex colorings. The authors also describe edge colorings, monochromatic and rainbow edge colorings, complete vertex colorings, several distinguishing vertex and edge colorings. Features of the Second Edition: The book can be used for a first course in graph theory as well as a graduate course The primary topic in the book is graph coloring The book begins with an introduction to graph theory so assumes no previous course The authors are the most widely-published team on graph theory Many new examples and exercises enhance the new edition

Author : Richard J. Trudeau
Publisher : Courier Corporation
Page : 224 pages
File Size : 48,7 Mb
Release : 2013-04-15
Category : Mathematics
ISBN : 9780486318660

Get Book

Introduction to Graph Theory by Richard J. Trudeau Pdf

Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.

Author : Indubala I Satija
Publisher : Morgan & Claypool Publishers
Page : 350 pages
File Size : 45,8 Mb
Release : 2016-09-06
Category : Science
ISBN : 9781681741178

Get Book

The Butterfly in the Quantum World by Indubala I Satija Pdf

Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.

Author : Robin Wilson,John J. Watkins,David J. Parks
Publisher : Princeton University Press
Page : 320 pages
File Size : 50,9 Mb
Release : 2023-01-17
Category : Computers
ISBN : 9780691194028

Get Book

Graph Theory in America by Robin Wilson,John J. Watkins,David J. Parks Pdf

How a new mathematical field grew and matured in America Graph Theory in America focuses on the development of graph theory in North America from 1876 to 1976. At the beginning of this period, James Joseph Sylvester, perhaps the finest mathematician in the English-speaking world, took up his appointment as the first professor of mathematics at the Johns Hopkins University, where his inaugural lecture outlined connections between graph theory, algebra, and chemistry—shortly after, he introduced the word graph in our modern sense. A hundred years later, in 1976, graph theory witnessed the solution of the long-standing four color problem by Kenneth Appel and Wolfgang Haken of the University of Illinois. Tracing graph theory’s trajectory across its first century, this book looks at influential figures in the field, both familiar and less known. Whereas many of the featured mathematicians spent their entire careers working on problems in graph theory, a few such as Hassler Whitney started there and then moved to work in other areas. Others, such as C. S. Peirce, Oswald Veblen, and George Birkhoff, made excursions into graph theory while continuing their focus elsewhere. Between the main chapters, the book provides short contextual interludes, describing how the American university system developed and how graph theory was progressing in Europe. Brief summaries of specific publications that influenced the subject’s development are also included. Graph Theory in America tells how a remarkable area of mathematics landed on American soil, took root, and flourished.

Author : Martin Charles Golumbic
Publisher : Elsevier
Page : 306 pages
File Size : 43,9 Mb
Release : 2014-05-10
Category : Mathematics
ISBN : 9781483271972

Get Book

Algorithmic Graph Theory and Perfect Graphs by Martin Charles Golumbic Pdf

Algorithmic Graph Theory and Perfect Graphs provides an introduction to graph theory through practical problems. This book presents the mathematical and algorithmic properties of special classes of perfect graphs. Organized into 12 chapters, this book begins with an overview of the graph theoretic notions and the algorithmic design. This text then examines the complexity analysis of computer algorithm and explains the differences between computability and computational complexity. Other chapters consider the parameters and properties of a perfect graph and explore the class of perfect graphs known as comparability graph or transitively orientable graphs. This book discusses as well the two characterizations of triangulated graphs, one algorithmic and the other graph theoretic. The final chapter deals with the method of performing Gaussian elimination on a sparse matrix wherein an arbitrary choice of pivots may result in the filling of some zero positions with nonzeros. This book is a valuable resource for mathematicians and computer scientists.

Author : Norman Biggs,E. Keith Lloyd,Robin J. Wilson
Publisher : Oxford University Press
Page : 260 pages
File Size : 55,6 Mb
Release : 1986
Category : Mathematics
ISBN : 0198539169

Get Book

Graph Theory, 1736-1936 by Norman Biggs,E. Keith Lloyd,Robin J. Wilson Pdf

First published in 1976, this book has been widely acclaimed as a major and enlivening contribution to the history of mathematics. The updated and corrected paperback contains extracts from the original writings of mathematicians who contributed to the foundations of graph theory. The author's commentary links each piece historically and frames the whole with explanations of the relevant mathematical terminology and notation.

Author : Stevo Todorcevic
Publisher : Princeton University Press
Page : 296 pages
File Size : 50,8 Mb
Release : 2010-07-01
Category : Mathematics
ISBN : 9781400835409

Get Book

Introduction to Ramsey Spaces (AM-174) by Stevo Todorcevic Pdf

Ramsey theory is a fast-growing area of combinatorics with deep connections to other fields of mathematics such as topological dynamics, ergodic theory, mathematical logic, and algebra. The area of Ramsey theory dealing with Ramsey-type phenomena in higher dimensions is particularly useful. Introduction to Ramsey Spaces presents in a systematic way a method for building higher-dimensional Ramsey spaces from basic one-dimensional principles. It is the first book-length treatment of this area of Ramsey theory, and emphasizes applications for related and surrounding fields of mathematics, such as set theory, combinatorics, real and functional analysis, and topology. In order to facilitate accessibility, the book gives the method in its axiomatic form with examples that cover many important parts of Ramsey theory both finite and infinite. An exciting new direction for combinatorics, this book will interest graduate students and researchers working in mathematical subdisciplines requiring the mastery and practice of high-dimensional Ramsey theory.

Author : Maarten van Steen
Publisher : Maarten Van Steen
Page : 285 pages
File Size : 52,9 Mb
Release : 2010
Category : Graph theory
ISBN : 9081540610

Get Book

Graph Theory and Complex Networks by Maarten van Steen Pdf

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.

Author : Koh Khee Meng,Dong Fengming,Tay Eng Guan
Publisher : World Scientific Publishing Company
Page : 244 pages
File Size : 50,7 Mb
Release : 2007-03-15
Category : Mathematics
ISBN : 9789813101630

Get Book

Introduction to Graph Theory by Koh Khee Meng,Dong Fengming,Tay Eng Guan Pdf

Graph theory is an area in discrete mathematics which studies configurations (called graphs) involving a set of vertices interconnected by edges. This book is intended as a general introduction to graph theory and, in particular, as a resource book for junior college students and teachers reading and teaching the subject at H3 Level in the new Singapore mathematics curriculum for junior college. The book builds on the verity that graph theory at this level is a subject that lends itself well to the development of mathematical reasoning and proof.