Introduction to Graph Theory

Author: Richard J. Trudeau

Publisher: Courier Corporation

ISBN: 0486318664

Category: Mathematics

Page: 224

View: 6517

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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.

Introduction to Graph Theory

Author: Douglas West

Publisher: Prentice Hall

ISBN: 9780131437371

Category: Mathematics

Page: 608

View: 659

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This book fills a need for a thorough introduction to graph theory that features both the understanding and writing of proofs about graphs. Verification that algorithms work is emphasized more than their complexity.An effective use of examples, and huge number of interesting exercises, demonstrate the topics of trees and distance, matchings and factors, connectivity and paths, graph coloring, edges and cycles, and planar graphs.For those who need to learn to make coherent arguments in the fields of mathematics and computer science.

Introduction to Graph Theory

Author: Robin J. Wilson

Publisher: Pearson Higher Ed

ISBN: 1292122552

Category: Mathematics

Page: 192

View: 7614

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In recent years graph theory has emerged as a subject in its own right, as well as being an important mathematical tool in such diverse subjects as operational research, chemistry, sociology and genetics. Robin Wilson’s book has been widely used as a text for undergraduate courses in mathematics, computer science and economics, and as a readable introduction to the subject for non-mathematicians. The opening chapters provide a basic foundation course, containing definitions and examples, connectedness, Eulerian and Hamiltonian paths and cycles, and trees, with a range of applications. This is followed by two chapters on planar graphs and colouring, with special reference to the four-colour theorem. The next chapter deals with transversal theory and connectivity, with applications to network flows. A final chapter on matroid theory ties together material from earlier chapters, and an appendix discusses algorithms and their efficiency.

Introduction to Graph Theory

H3 Mathematics

Author: Khee Meng Koh,F. M. Dong,Eng Guan Tay

Publisher: World Scientific

ISBN: 9812705252

Category: Mathematics

Page: 228

View: 1889

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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.

Introduction to Graph Theory

Solutions Manual

Author: Koh Khee Meng,Dong Fengming,Tay Eng Guan

Publisher: World Scientific Publishing Company

ISBN: 9813101458

Category: Mathematics

Page: 260

View: 1849

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This is a companion to the book Introduction to Graph Theory (World Scientific, 2006). The student who has worked on the problems will find the solutions presented useful as a check and also as a model for rigorous mathematical writing. For ease of reference, each chapter recaps some of the important concepts and/or formulae from the earlier book.

A First Course in Graph Theory

Author: Gary Chartrand,Ping Zhang

Publisher: Courier Corporation

ISBN: 0486297306

Category: Mathematics

Page: 464

View: 4105

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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.

Introduction to Graph and Hypergraph Theory

Author: Vitaly Ivanovich Voloshin

Publisher: N.A

ISBN: 9781606923726

Category: Graph theory

Page: 287

View: 8786

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This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. Structurally, the text is divided into two parts where Part II is the generalisation of Part I. The first part discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring. The second part considers generalisations of Part I and discusses hypertrees, bipartite hypergraphs, hypercycles, chordal hypergraphs, planar hypergraphs and hypergraph colouring. There is an interaction between the parts and within the parts to show how ideas of generalisations work. The main point is to exhibit the ways of generalisations and interactions of mathematical concepts from the very simple to the most advanced. One of the features of this text is the duality of hypergraphs. This fundamental concept is missing in graph theory (and in its introductory teaching) because dual graphs are not properly graphs, they are hypergraphs. However, as Part II shows, the duality is a very powerful tool in understanding, simplifying and unifying many combinatorial relations; it is basically a look at the same structure from the opposite (vertices versus edges) point of view.

Introduction to Graph Theory

Author: Gary Chartrand,Ping Zhang

Publisher: McGraw-Hill Science, Engineering & Mathematics

ISBN: 9780072948622

Category: Mathematics

Page: 449

View: 9520

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A non-technical introduction to the field of graph theory and its applications. Presents a variety of proofs, plus challenging fun with mathematics.

A Walk Through Combinatorics

An Introduction to Enumeration and Graph Theory

Author: Mikl¢s B¢na

Publisher: World Scientific

ISBN: 9814335231

Category: Mathematics

Page: 546

View: 7129

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Suitable for an introductory combinatorics course lasting one or two semesters, this book includes an extensive list of problems, ranging from routine exercises to research questions. It walks the reader through the classic parts of combinatorial enumeration and graph theory, while also discussing some the progress made in the area.

A Beginner's Guide to Graph Theory

Author: W.D. Wallis

Publisher: Springer Science & Business Media

ISBN: 9780817645809

Category: Mathematics

Page: 260

View: 5672

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Concisely written, gentle introduction to graph theory suitable as a textbook or for self-study Graph-theoretic applications from diverse fields (computer science, engineering, chemistry, management science) 2nd ed. includes new chapters on labeling and communications networks and small worlds, as well as expanded beginner's material Many additional changes, improvements, and corrections resulting from classroom use

A Gentle Introduction to Graph Theory

Author: Valsamma K M

Publisher: N.A

ISBN: 9789383185634

Category:

Page: 200

View: 1163

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Graph theory is a subject which is gaining momentum in the syllabi of different Engineering, streams especially in Electrical Engineering, Computer Science, Information Technology, Communication Engineering, Environmental science & Material Physics. The book is tailor made to the needs of students of undergraduate courses in Mathematics, B.Tech, and Post Graduate courses in science and computer application of various universities. The topics covered in the book have been chosen with a view to easily bridging the knowledge gap in Mathematics that exist between students of various streams for a better understanding of the subject. However the book gives a compact yet rigorous treatment of the mathematical tool available for a general of study of graphs. The book is also designed to be self contained consisting of eight chapters. Each chapter contains a large number of illustrations with examples to explain definitions and theorems therein. To stimulate further learning interest, practice problem are inserted.

Introduction to Graph Theory

Author: Vitaly Ivanovich Voloshin

Publisher: Nova Science Pub Incorporated

ISBN: 9781606923740

Category: Mathematics

Page: 144

View: 2050

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Graph Theory is an important area of contemporary mathematics with many applications in computer science, genetics, chemistry, engineering, industry, business and in social sciences. It is a young science invented and developing for solving challenging problems of "computerised" society for which traditional areas of mathematics such as algebra or calculus are powerless. This book is for math and computer science majors, for students and representatives of many other disciplines (like bioinformatics, for example) taking the courses in graph theory, discrete mathematics, data structures, algorithms. It is also for anyone who wants to understand the basics of graph theory, or just is curious. No previous knowledge in graph theory or any other significant mathematics is required. The very basic facts from set theory, proof techniques and algorithms are sufficient to understand it; but even those are explained in the text. The book discusses the key concepts of graph theory with emphasis on trees, bipartite graphs, cycles, chordal graphs, planar graphs and graph colouring. The reader is conducted from the simplest examples, definitions and concepts, step by step, towards an understanding of a few most fundamental facts in the field. to show an interaction between the sections and chapters for the sake of integrity; clearly expose the essence and core of graph theory. The book may be used on undergraduate level for one semester introductory course. It includes many examples, figures and algorithms; each section ends with a set of exercises and a set of computer projects. The answers and hints to selected exercises are provided at the end of the book. The material has been tested in class during more than 20-years of teaching experience of the author.

Introductory Graph Theory

Author: Gary Chartrand

Publisher: Courier Corporation

ISBN: 0486134946

Category: Science

Page: 320

View: 2602

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Clear, lively style covers all basics of theory and application, including mathematical models, elementary graph theory, transportation problems, connection problems, party problems, diagraphs and mathematical models, games and puzzles, more.

A First Look at Graph Theory

Author: John Clark,Derek Allan Holton

Publisher: World Scientific

ISBN: 9789810204907

Category: Mathematics

Page: 330

View: 830

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This book is intended to be an introductory text for mathematics and computer science students at the second and third year levels in universities. It gives an introduction to the subject with sufficient theory for students at those levels, with emphasis on algorithms and applications.

A Friendly Introduction to Graph Theory

Author: Fred Buckley,Marty Lewinter

Publisher: N.A

ISBN: 9780130669490

Category: Mathematics

Page: 365

View: 2471

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This book introduces graph theory, a subject with a wide range of applications in real-work situations. This book is designed to be easily accessible to the novice, assuming no more than a good grasp of algebra to understand and relate to the concepts presented. Using many examples, illustrations, and figures, it provides an excellent foundation for the basic knowledge of graphs and their applications. This book includes an introductory chapter that reviews the tools necessary to understand the concepts of graphs, and then goes on to cover such topics as trees and bipartite graphs, distance and connectivity, Eulerian and Hamiltonian graphs, graph coloring, matrices, algorithms, planar graphs, and digraphs and networks. Graph theory has a wide range of applications; this book is useful for those in the fields of anthropology, computer science, chemistry, environmental conservation, fluid dynamics, psychology, sociology, traffic management, telecommunications, and business managers and strategists.

Graph Theory with Applications to Engineering and Computer Science

Author: Narsingh Deo

Publisher: Courier Dover Publications

ISBN: 0486820815

Category: Mathematics

Page: 496

View: 434

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Outstanding introductory treatment, geared toward advanced undergraduates and graduate students who require knowledge of graph theory. The first nine chapters constitute an excellent overview; the remaining chapters are more advanced and provide material for a variety of courses. 1974 edition.

Graph Theory and Its Applications

Author: Jonathan L. Gross,Jay Yellen,Mark Anderson

Publisher: CRC Press

ISBN: 0429757085

Category: Computers

Page: 577

View: 6509

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Graph Theory and Its Applications, Third Edition is the latest edition of the international, bestselling textbook for undergraduate courses in graph theory, yet it is expansive enough to be used for graduate courses as well. The textbook takes a comprehensive, accessible approach to graph theory, integrating careful exposition of classical developments with emerging methods, models, and practical needs. The authors’ unparalleled treatment is an ideal text 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. Features of the Third Edition Expanded coverage on several topics (e.g., applications of graph coloring and tree-decompositions) Provides better coverage of algorithms and algebraic and topological graph theory than any other text Incorporates several levels of carefully designed exercises that promote student retention and develop and sharpen problem-solving skills Includes supplementary exercises to develop problem-solving skills, solutions and hints, and a detailed appendix, which reviews the textbook’s topics About the Authors Jonathan L. Gross is a professor of computer science at Columbia University. His research interests include topology and graph theory. Jay Yellen is a professor of mathematics at Rollins College. His current areas of research include graph theory, combinatorics, and algorithms. Mark Anderson is also a mathematics professor at Rollins College. His research interest in graph theory centers on the topological or algebraic side.

Pearls in Graph Theory

A Comprehensive Introduction

Author: Nora Hartsfield,Gerhard Ringel

Publisher: Courier Corporation

ISBN: 0486315525

Category: Mathematics

Page: 272

View: 3371

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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.

Graph Theory and Complex Networks

An Introduction

Author: Maarten van Steen

Publisher: Maarten Van Steen

ISBN: 9789081540612

Category: Graph theory

Page: 285

View: 6660

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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.