Fundamentals Of Graph Theory

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Fundamentals of Graph Theory

Author : Allan Bickle
Publisher : American Mathematical Soc.
ISBN 13 : 1470453428
Total Pages : 354 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Fundamentals of Graph Theory by : Allan Bickle

Download or read book Fundamentals of Graph Theory written by Allan Bickle and published by American Mathematical Soc.. This book was released on 2020-03-10 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practical applications that motivate their development, and which are illustrated with examples that show how to apply major theorems in practice. This includes the process of finding a brute force solution (case-checking) when an elegant solution is not apparent. With over 1200 exercises, internet resources (e.g., the OEIS for counting problems), helpful appendices, and a detailed guide to different course outlines, this book provides a versatile and convenient tool for the needs of instructors at a large variety of institutions.

Fundamentals of Graph Theory

Author : Allan Bickle
Publisher :
ISBN 13 : 9781470455491
Total Pages : 354 pages
Book Rating : 4.4/5 (554 download)

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Book Synopsis Fundamentals of Graph Theory by : Allan Bickle

Download or read book Fundamentals of Graph Theory written by Allan Bickle and published by . This book was released on with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph theory is a fascinating and inviting branch of mathematics. Many problems are easy to state and have natural visual representations, inviting exploration by new students and professional mathematicians. The goal of this textbook is to present the fundamentals of graph theory to a wide range of readers. The book contains many significant recent results in graph theory, presented using up-to-date notation. The author included the shortest, most elegant, most intuitive proofs for modern and classic results while frequently presenting them in new ways. Major topics are introduced with practi.

Chemical Graph Theory

Author : D Bonchev
Publisher : Routledge
ISBN 13 : 1351461591
Total Pages : 310 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Chemical Graph Theory by : D Bonchev

Download or read book Chemical Graph Theory written by D Bonchev and published by Routledge. This book was released on 2018-05-11 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume presents the fundamentals of graph theory and then goes on to discuss specific chemical applications. Chapter 1 provides a historical setting for the current upsurge of interest in chemical graph theory. Chapter 2 gives a full background of the basic ideas and mathematical formalism of graph theory and includes such chemically relevant notions as connectedness, graph matrix representations, metric properties, symmetry and operations on graphs. This is followed by a discussion on chemical nomenclature and the trends in its rationalization by using graph theory, which has important implications for the storage and retrieval of chemical information. This volume also contains a detailed discussion of the relevance of graph-theoretical polynomials; it describes methodologies for the enumeration of isomers, incorporating the classical Polya method, as well as more recent approaches.

Fundamentals of Domination in Graphs

Author : Teresa W. Haynes
Publisher : CRC Press
ISBN 13 : 1482246589
Total Pages : 465 pages
Book Rating : 4.4/5 (822 download)

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Book Synopsis Fundamentals of Domination in Graphs by : Teresa W. Haynes

Download or read book Fundamentals of Domination in Graphs written by Teresa W. Haynes and published by CRC Press. This book was released on 2013-12-16 with total page 465 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Provides the first comprehensive treatment of theoretical, algorithmic, and application aspects of domination in graphs-discussing fundamental results and major research accomplishments in an easy-to-understand style. Includes chapters on domination algorithms and NP-completeness as well as frameworks for domination."

Fundamentals of Brain Network Analysis

Author : Alex Fornito
Publisher : Academic Press
ISBN 13 : 0124081185
Total Pages : 496 pages
Book Rating : 4.1/5 (24 download)

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Book Synopsis Fundamentals of Brain Network Analysis by : Alex Fornito

Download or read book Fundamentals of Brain Network Analysis written by Alex Fornito and published by Academic Press. This book was released on 2016-03-04 with total page 496 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fundamentals of Brain Network Analysis is a comprehensive and accessible introduction to methods for unraveling the extraordinary complexity of neuronal connectivity. From the perspective of graph theory and network science, this book introduces, motivates and explains techniques for modeling brain networks as graphs of nodes connected by edges, and covers a diverse array of measures for quantifying their topological and spatial organization. It builds intuition for key concepts and methods by illustrating how they can be practically applied in diverse areas of neuroscience, ranging from the analysis of synaptic networks in the nematode worm to the characterization of large-scale human brain networks constructed with magnetic resonance imaging. This text is ideally suited to neuroscientists wanting to develop expertise in the rapidly developing field of neural connectomics, and to physical and computational scientists wanting to understand how these quantitative methods can be used to understand brain organization. - Winner of the 2017 PROSE Award in Biomedicine & Neuroscience and the 2017 British Medical Association (BMA) Award in Neurology - Extensively illustrated throughout by graphical representations of key mathematical concepts and their practical applications to analyses of nervous systems - Comprehensively covers graph theoretical analyses of structural and functional brain networks, from microscopic to macroscopic scales, using examples based on a wide variety of experimental methods in neuroscience - Designed to inform and empower scientists at all levels of experience, and from any specialist background, wanting to use modern methods of network science to understand the organization of the brain

Fundamentals of Algebraic Graph Transformation

Author : Hartmut Ehrig
Publisher : Springer Science & Business Media
ISBN 13 : 3540311882
Total Pages : 383 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Fundamentals of Algebraic Graph Transformation by : Hartmut Ehrig

Download or read book Fundamentals of Algebraic Graph Transformation written by Hartmut Ehrig and published by Springer Science & Business Media. This book was released on 2006-05-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Chromatic Graph Theory

Author : Gary Chartrand
Publisher : CRC Press
ISBN 13 : 0429798288
Total Pages : 503 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Chromatic Graph Theory by : Gary Chartrand

Download or read book Chromatic Graph Theory written by Gary Chartrand and published by CRC Press. This book was released on 2019-11-28 with total page 503 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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

Introduction to Graph Theory

Author : Richard J. Trudeau
Publisher : Courier Corporation
ISBN 13 : 0486318664
Total Pages : 242 pages
Book Rating : 4.4/5 (863 download)

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Book Synopsis Introduction to Graph Theory by : Richard J. Trudeau

Download or read book Introduction to Graph Theory written by Richard J. Trudeau and published by Courier Corporation. This book was released on 2013-04-15 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Graphs

Author : K. Thulasiraman
Publisher : John Wiley & Sons
ISBN 13 : 1118030257
Total Pages : 480 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Graphs by : K. Thulasiraman

Download or read book Graphs written by K. Thulasiraman and published by John Wiley & Sons. This book was released on 2011-03-29 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: This adaptation of an earlier work by the authors is a graduate text and professional reference on the fundamentals of graph theory. It covers the theory of graphs, its applications to computer networks and the theory of graph algorithms. Also includes exercises and an updated bibliography.

Graph Theory Applications

Author : L.R. Foulds
Publisher : Springer Science & Business Media
ISBN 13 : 1461209331
Total Pages : 389 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Graph Theory Applications by : L.R. Foulds

Download or read book Graph Theory Applications written by L.R. Foulds and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 389 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first part of this text covers the main graph theoretic topics: connectivity, trees, traversability, planarity, colouring, covering, matching, digraphs, networks, matrices of a graph, graph theoretic algorithms, and matroids. These concepts are then applied in the second part to problems in engineering, operations research, and science as well as to an interesting set of miscellaneous problems, thus illustrating their broad applicability. Every effort has been made to present applications that use not merely the notation and terminology of graph theory, but also its actual mathematical results. Some of the applications, such as in molecular evolution, facilities layout, and graffic network design, have never appeared before in book form. Written at an advanced undergraduate to beginning graduate level, this book is suitable for students of mathematics, engineering, operations research, computer science, and physical sciences as well as for researchers and practitioners with an interest in graph theoretic modelling.

A First Course in Graph Theory

Author : Gary Chartrand
Publisher : Courier Corporation
ISBN 13 : 0486297306
Total Pages : 466 pages
Book Rating : 4.4/5 (862 download)

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Book Synopsis A First Course in Graph Theory by : Gary Chartrand

Download or read book A First Course in Graph Theory written by Gary Chartrand and published by Courier Corporation. This book was released on 2013-05-20 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Combinatorics and Graph Theory

Author : John Harris
Publisher : Springer Science & Business Media
ISBN 13 : 0387797114
Total Pages : 392 pages
Book Rating : 4.3/5 (877 download)

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Book Synopsis Combinatorics and Graph Theory by : John Harris

Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.

Domination in Graphs

Author : TeresaW. Haynes
Publisher : Routledge
ISBN 13 : 1351454641
Total Pages : 519 pages
Book Rating : 4.3/5 (514 download)

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Book Synopsis Domination in Graphs by : TeresaW. Haynes

Download or read book Domination in Graphs written by TeresaW. Haynes and published by Routledge. This book was released on 2017-11-22 with total page 519 pages. Available in PDF, EPUB and Kindle. Book excerpt: ""Presents the latest in graph domination by leading researchers from around the world-furnishing known results, open research problems, and proof techniques. Maintains standardized terminology and notation throughout for greater accessibility. Covers recent developments in domination in graphs and digraphs, dominating functions, combinatorial problems on chessboards, and more.

Modern Graph Theory

Author : Bela Bollobas
Publisher : Springer Science & Business Media
ISBN 13 : 1461206197
Total Pages : 408 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Modern Graph Theory by : Bela Bollobas

Download or read book Modern Graph Theory written by Bela Bollobas and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Fundamentals of Number Theory

Author : William J. LeVeque
Publisher : Courier Corporation
ISBN 13 : 0486141500
Total Pages : 292 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Fundamentals of Number Theory by : William J. LeVeque

Download or read book Fundamentals of Number Theory written by William J. LeVeque and published by Courier Corporation. This book was released on 2014-01-05 with total page 292 pages. Available in PDF, EPUB and Kindle. Book excerpt: This excellent textbook introduces the basics of number theory, incorporating the language of abstract algebra. A knowledge of such algebraic concepts as group, ring, field, and domain is not assumed, however; all terms are defined and examples are given — making the book self-contained in this respect. The author begins with an introductory chapter on number theory and its early history. Subsequent chapters deal with unique factorization and the GCD, quadratic residues, number-theoretic functions and the distribution of primes, sums of squares, quadratic equations and quadratic fields, diophantine approximation, and more. Included are discussions of topics not always found in introductory texts: factorization and primality of large integers, p-adic numbers, algebraic number fields, Brun's theorem on twin primes, and the transcendence of e, to mention a few. Readers will find a substantial number of well-chosen problems, along with many notes and bibliographical references selected for readability and relevance. Five helpful appendixes — containing such study aids as a factor table, computer-plotted graphs, a table of indices, the Greek alphabet, and a list of symbols — and a bibliography round out this well-written text, which is directed toward undergraduate majors and beginning graduate students in mathematics. No post-calculus prerequisite is assumed. 1977 edition.

Graphs, Networks and Algorithms

Author : Dieter Jungnickel
Publisher : Springer Science & Business Media
ISBN 13 : 3662038226
Total Pages : 597 pages
Book Rating : 4.6/5 (62 download)

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Book Synopsis Graphs, Networks and Algorithms by : Dieter Jungnickel

Download or read book Graphs, Networks and Algorithms written by Dieter Jungnickel and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 597 pages. Available in PDF, EPUB and Kindle. Book excerpt: Revised throughout Includes new chapters on the network simplex algorithm and a section on the five color theorem Recent developments are discussed

Fundamentals of Ramsey Theory

Author : Aaron Robertson
Publisher : CRC Press
ISBN 13 : 0429775911
Total Pages : 256 pages
Book Rating : 4.4/5 (297 download)

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Book Synopsis Fundamentals of Ramsey Theory by : Aaron Robertson

Download or read book Fundamentals of Ramsey Theory written by Aaron Robertson and published by CRC Press. This book was released on 2021-06-17 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: Ramsey theory is a fascinating topic. The author shares his view of the topic in this contemporary overview of Ramsey theory. He presents from several points of view, adding intuition and detailed proofs, in an accessible manner unique among most books on the topic. This book covers all of the main results in Ramsey theory along with results that have not appeared in a book before. The presentation is comprehensive and reader friendly. The book covers integer, graph, and Euclidean Ramsey theory with many proofs being combinatorial in nature. The author motivates topics and discussion, rather than just a list of theorems and proofs. In order to engage the reader, each chapter has a section of exercises. This up-to-date book introduces the field of Ramsey theory from several different viewpoints so that the reader can decide which flavor of Ramsey theory best suits them. Additionally, the book offers: A chapter providing different approaches to Ramsey theory, e.g., using topological dynamics, ergodic systems, and algebra in the Stone-Čech compactification of the integers. A chapter on the probabilistic method since it is quite central to Ramsey-type numbers. A unique chapter presenting some applications of Ramsey theory. Exercises in every chapter The intended audience consists of students and mathematicians desiring to learn about Ramsey theory. An undergraduate degree in mathematics (or its equivalent for advanced undergraduates) and a combinatorics course is assumed. TABLE OF CONENTS Preface List of Figures List of Tables Symbols 1. Introduction 2. Integer Ramsey Theory 3. Graph Ramsey Theory 4. Euclidean Ramsey Theory 5. Other Approaches to Ramsey Theory 6. The Probabilistic Method 7. Applications Bibliography Index Biography Aaron Robertson received his Ph.D. in mathematics from Temple University under the guidance of his advisor Doron Zeilberger. Upon finishing his Ph.D. he started at Colgate University in upstate New York where he is currently Professor of Mathematics. He also serves as Associate Managing editor of the journal Integers. After a brief detour into the world of permutation patterns, he has focused most of his research on Ramsey theory.