Introduction To Graph And Hypergraph Theory
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Introduction To Graph And Hypergraph Theory
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Author : Vitaly Ivanovich Voloshin
language : en
Publisher:
Release Date : 2009
Introduction To Graph And Hypergraph Theory written by Vitaly Ivanovich Voloshin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009 with Graph theory categories.
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.
Hypergraph Theory
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Author : Alain Bretto
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-04-17
Hypergraph Theory written by Alain Bretto and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-17 with Mathematics categories.
This book provides an introduction to hypergraphs, its aim being to overcome the lack of recent manuscripts on this theory. In the literature hypergraphs have many other names such as set systems and families of sets. This work presents the theory of hypergraphs in its most original aspects, while also introducing and assessing the latest concepts on hypergraphs. The variety of topics, their originality and novelty are intended to help readers better understand the hypergraphs in all their diversity in order to perceive their value and power as mathematical tools. This book will be a great asset to upper-level undergraduate and graduate students in computer science and mathematics. It has been the subject of an annual Master's course for many years, making it also ideally suited to Master's students in computer science, mathematics, bioinformatics, engineering, chemistry, and many other fields. It will also benefit scientists, engineers and anyone else who wants to understand hypergraphs theory.
Combinatorics And Graph Theory
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Author : John Harris
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-04-03
Combinatorics And Graph Theory written by John Harris and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-04-03 with Mathematics categories.
There are certain rules that one must abide by in order to create a successful sequel. — Randy Meeks, from the trailer to Scream 2 While we may not follow the precise rules that Mr. Meeks had in mind for s- cessful sequels, we have made a number of changes to the text in this second edition. In the new edition, we continue to introduce new topics with concrete - amples, we provide complete proofs of almost every result, and we preserve the book’sfriendlystyle andlivelypresentation,interspersingthetextwith occasional jokes and quotations. The rst two chapters, on graph theory and combinatorics, remain largely independent, and may be covered in either order. Chapter 3, on in nite combinatorics and graphs, may also be studied independently, although many readers will want to investigate trees, matchings, and Ramsey theory for nite sets before exploring these topics for in nite sets in the third chapter. Like the rst edition, this text is aimed at upper-division undergraduate students in mathematics, though others will nd much of interest as well. It assumes only familiarity with basic proof techniques, and some experience with matrices and in nite series. The second edition offersmany additionaltopics for use in the classroom or for independentstudy. Chapter 1 includesa new sectioncoveringdistance andrelated notions in graphs, following an expanded introductory section. This new section also introduces the adjacency matrix of a graph, and describes its connection to important features of the graph.
Applications Of Hyperstructure Theory
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Author : P. Corsini
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Applications Of Hyperstructure Theory written by P. Corsini and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
This book presents some of the numerous applications of hyperstructures, especially those that were found and studied in the last fifteen years. There are applications to the following subjects: 1) geometry; 2) hypergraphs; 3) binary relations; 4) lattices; 5) fuzzy sets and rough sets; 6) automata; 7) cryptography; 8) median algebras, relation algebras; 9) combinatorics; 10) codes; 11) artificial intelligence; 12) probabilities. Audience: Graduate students and researchers.
Graph Theory And Its Applications Second Edition
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Author : Jonathan L. Gross
language : en
Publisher: CRC Press
Release Date : 2005-09-22
Graph Theory And Its Applications Second Edition written by Jonathan L. Gross and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-09-22 with Mathematics categories.
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? New chapters on measurement and analytic graph theory Supplementary exercises in each chapter - ideal for reinforcing, reviewing, and testing. Solutions and hints, often illustrated with figures, to selected exercises - nearly 50 pages worth Reorganization and extensive revisions in more than half of the existing chapters for smoother flow of the exposition Foreshadowing - the first three chapters now preview a number of concepts, mostly via the exercises, to pique the interest of reader Gross 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.
Introduction To Random Graphs
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Author : Alan Frieze
language : en
Publisher: Cambridge University Press
Release Date : 2016
Introduction To Random Graphs written by Alan Frieze and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Mathematics categories.
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Topics In Topological Graph Theory
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Author : Lowell W. Beineke
language : en
Publisher: Cambridge University Press
Release Date : 2009-07-09
Topics In Topological Graph Theory written by Lowell W. Beineke and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2009-07-09 with Mathematics categories.
The use of topological ideas to explore various aspects of graph theory, and vice versa, is a fruitful area of research. There are links with other areas of mathematics, such as design theory and geometry, and increasingly with such areas as computer networks where symmetry is an important feature. Other books cover portions of the material here, but there are no other books with such a wide scope. This book contains fifteen expository chapters written by acknowledged international experts in the field. Their well-written contributions have been carefully edited to enhance readability and to standardize the chapter structure, terminology and notation throughout the book. To help the reader, there is an extensive introductory chapter that covers the basic background material in graph theory and the topology of surfaces. Each chapter concludes with an extensive list of references.
Fractional Graph Theory
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Author : Edward R. Scheinerman
language : en
Publisher: Courier Corporation
Release Date : 2013-04-29
Fractional Graph Theory written by Edward R. Scheinerman and has been published by Courier Corporation this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-29 with Mathematics categories.
This volume explains the general theory of hypergraphs and presents in-depth coverage of fundamental and advanced topics: fractional matching, fractional coloring, fractional edge coloring, fractional arboricity via matroid methods, fractional isomorphism, and more. 1997 edition.
Graph Theory With Applications
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Author : John Adrian Bondy
language : en
Publisher: London : Macmillan Press
Release Date : 1976
Graph Theory With Applications written by John Adrian Bondy and has been published by London : Macmillan Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Mathematics categories.