Matrices and Graphs in Geometry

Author: Miroslav Fiedler

Publisher: Cambridge University Press

ISBN: 0521461936

Category: Mathematics

Page: 197

View: 804

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This series is devoted to significant topics or themes that have wide application in mathematics or mathematical science and for which a detailed development of the abstract theory is less important than a thorough and concrete exploration of the implications and applications. Books in the Encyclopedia of Mathematics and Its Applications cover their subjects comprehensively. Less important results may be summarized as exercises at the ends of chapters. Each book contains an extensive bibliography. Thus the volumes are encyclopedic references or manageable guides to major subjects.

Topics in Algebraic Graph Theory

Author: Lowell W. Beineke,Robin J. Wilson

Publisher: Cambridge University Press

ISBN: 9780521801973

Category: Mathematics

Page: 276

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There is no other book with such a wide scope of both areas of algebraic graph theory.

Graphs and Matrices

Author: Ravindra B. Bapat

Publisher: Springer

ISBN: 1447165691

Category: Mathematics

Page: 193

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This new edition illustrates the power of linear algebra in the study of graphs. The emphasis on matrix techniques is greater than in other texts on algebraic graph theory. Important matrices associated with graphs (for example, incidence, adjacency and Laplacian matrices) are treated in detail. Presenting a useful overview of selected topics in algebraic graph theory, early chapters of the text focus on regular graphs, algebraic connectivity, the distance matrix of a tree, and its generalized version for arbitrary graphs, known as the resistance matrix. Coverage of later topics include Laplacian eigenvalues of threshold graphs, the positive definite completion problem and matrix games based on a graph. Such an extensive coverage of the subject area provides a welcome prompt for further exploration. The inclusion of exercises enables practical learning throughout the book. In the new edition, a new chapter is added on the line graph of a tree, while some results in Chapter 6 on Perron-Frobenius theory are reorganized. Whilst this book will be invaluable to students and researchers in graph theory and combinatorial matrix theory, it will also benefit readers in the sciences and engineering.

Combinatorial Matrix Classes

Author: Richard A. Brualdi

Publisher: Cambridge University Press

ISBN: 0521865654

Category: Mathematics

Page: 544

View: 8853

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A natural sequel to the author's previous book Combinatorial Matrix Theory written with H. J. Ryser, this is the first book devoted exclusively to existence questions, constructive algorithms, enumeration questions, and other properties concerning classes of matrices of combinatorial significance. Several classes of matrices are thoroughly developed including the classes of matrices of 0's and 1's with a specified number of 1's in each row and column (equivalently, bipartite graphs with a specified degree sequence), symmetric matrices in such classes (equivalently, graphs with a specified degree sequence), tournament matrices with a specified number of 1's in each row (equivalently, tournaments with a specified score sequence), nonnegative matrices with specified row and column sums, and doubly stochastic matrices. Most of this material is presented for the first time in book format and the chapter on doubly stochastic matrices provides the most complete development of the topic to date.


Matroids: A Geometric Introduction

Author: Gary Gordon,Jennifer McNulty

Publisher: Cambridge University Press

ISBN: 0521145686

Category: Language Arts & Disciplines

Page: 393

View: 4207

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This friendly introduction helps undergraduate students understand and appreciate matroid theory and its connections to geometry.

Combinatorial Matrix Theory

Author: Richard A. Brualdi,Herbert J. Ryser

Publisher: Cambridge University Press

ISBN: 9780521322652

Category: Mathematics

Page: 367

View: 363

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The book deals with the many connections between matrices, graphs, diagraphs and bipartite graphs. The basic theory of network flows is developed in order to obtain existence theorems for matrices with prescribed combinatorical properties and to obtain various matrix decomposition theorems. Other chapters cover the permanent of a matrix and Latin squares. The book ends by considering algebraic characterizations of combinatorical properties and the use of combinatorial arguments in proving classical algebraic theorems, including the Cayley-Hamilton Theorem and the Jorda Canonical Form.

Topics in Matroid Theory

Author: Leonidas S. Pitsoulis

Publisher: Springer Science & Business Media

ISBN: 1461489571

Category: Mathematics

Page: 127

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Topics in Matroid Theory provides a brief introduction to matroid theory with an emphasis on algorithmic consequences.Matroid theory is at the heart of combinatorial optimization and has attracted various pioneers such as Edmonds, Tutte, Cunningham and Lawler among others. Matroid theory encompasses matrices, graphs and other combinatorial entities under a common, solid algebraic framework, thereby providing the analytical tools to solve related difficult algorithmic problems. The monograph contains a rigorous axiomatic definition of matroids along with other necessary concepts such as duality, minors, connectivity and representability as demonstrated in matrices, graphs and transversals. The author also presents a deep decomposition result in matroid theory that provides a structural characterization of graphic matroids, and show how this can be extended to signed-graphic matroids, as well as the immediate algorithmic consequences.

Eigenspaces of Graphs

Author: Dragoš M. Cvetković,Peter Rowlinson,Slobodan Simic

Publisher: Cambridge University Press

ISBN: 9780521573528

Category: Mathematics

Page: 258

View: 5059

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This book describes the spectral theory of finite graphs.

Encyclopedia of Distances

Author: Michel Marie Deza,Elena Deza

Publisher: Springer

ISBN: 3662443422

Category: Mathematics

Page: 733

View: 5768

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This updated and revised third edition of the leading reference volume on distance metrics includes new items from very active research areas in the use of distances and metrics such as geometry, graph theory, probability theory and analysis. Among the new topics included are, for example, polyhedral metric space, nearness matrix problems, distances between belief assignments, distance-related animal settings, diamond-cutting distances, natural units of length, Heidegger’s de-severance distance, and brain distances. The publication of this volume coincides with intensifying research efforts into metric spaces and especially distance design for applications. Accurate metrics have become a crucial goal in computational biology, image analysis, speech recognition and information retrieval. Leaving aside the practical questions that arise during the selection of a ‘good’ distance function, this work focuses on providing the research community with an invaluable comprehensive listing of the main available distances. As well as providing standalone introductions and definitions, the encyclopedia facilitates swift cross-referencing with easily navigable bold-faced textual links to core entries. In addition to distances themselves, the authors have collated numerous fascinating curiosities in their Who’s Who of metrics, including distance-related notions and paradigms that enable applied mathematicians in other sectors to deploy research tools that non-specialists justly view as arcane. In expanding access to these techniques, and in many cases enriching the context of distances themselves, this peerless volume is certain to stimulate fresh research.

Permanents

Author: Henryk Minc

Publisher: Cambridge University Press

ISBN: 9780521302265

Category: Mathematics

Page: 224

View: 9641

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The purpose of this book, which was first published in 1978, is to give a complete account of the theory of permanents, their history and applications. This volume was the first complete account of the theory of permanents, covering virtually the whole of the subject, a feature that no simple survey of the theory of matrices can even attempt. The work also contains many results stated without formal proofs. This book can be used as a textbook at the advanced undergraduate or graduate level. The only prerequisites are a standard undergraduate course in the theory of matrices and a measure of mathematical maturity.

Codes and Automata

Author: Jean Berstel,Dominique Perrin,Christophe Reutenauer

Publisher: Cambridge University Press

ISBN: 052188831X

Category: Mathematics

Page: 619

View: 4534

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This major revision of Berstel and Perrin's classic Theory of Codes has been rewritten with a more modern focus and a much broader coverage of the subject. The concept of unambiguous automata, which is intimately linked with that of codes, now plays a significant role throughout the book, reflecting developments of the last 20 years. This is complemented by a discussion of the connection between codes and automata, and new material from the field of symbolic dynamics. The authors have also explored links with more practical applications, including data compression and cryptography. The treatment remains self-contained: there is background material on discrete mathematics, algebra and theoretical computer science. The wealth of exercises and examples make it ideal for self-study or courses. In summary, this is a comprehensive reference on the theory of variable-length codes and their relation to automata.

Graphs on Surfaces and Their Applications

Author: Sergei K. Lando,Alexander K. Zvonkin

Publisher: Springer Science & Business Media

ISBN: 3540383611

Category: Mathematics

Page: 455

View: 9160

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Graphs drawn on two-dimensional surfaces have always attracted researchers by their beauty and by the variety of difficult questions to which they give rise. The theory of such embedded graphs, which long seemed rather isolated, has witnessed the appearance of entirely unexpected new applications in recent decades, ranging from Galois theory to quantum gravity models, and has become a kind of a focus of a vast field of research. The book provides an accessible introduction to this new domain, including such topics as coverings of Riemann surfaces, the Galois group action on embedded graphs (Grothendieck's theory of "dessins d'enfants"), the matrix integral method, moduli spaces of curves, the topology of meromorphic functions, and combinatorial aspects of Vassiliev's knot invariants and, in an appendix by Don Zagier, the use of finite group representation theory. The presentation is concrete throughout, with numerous figures, examples (including computer calculations) and exercises, and should appeal to both graduate students and researchers.

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 9972

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This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Anthony Hilton,John Talbot

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 4013

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Graph Classes

A Survey

Author: Andreas Brandstãdt,Van Bang Le,Jeremy P. Spinrad

Publisher: SIAM

ISBN: 089871432X

Category: Mathematics

Page: 304

View: 2138

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The definitive encyclopedia for the literature on graph classes.


Probabilistic Methods in Combinatorial Analysis

Author: Vladimir Nikolaevich Sachkov

Publisher: Cambridge University Press

ISBN: 9780521455121

Category: Mathematics

Page: 246

View: 1100

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This work explores the role of probabilistic methods for solving combinatorial problems. The subjects studied are nonnegative matrices, partitions and mappings of finite sets, with special emphasis on permutations and graphs, and equivalence classes specified on sequences of finite length consisting of elements of partially ordered sets; these define the probabilistic setting of Sachkov's general combinatorial scheme. The author pays special attention to using probabilistic methods to obtain asymptotic formulae that are difficult to derive using combinatorial methods. This important book describes many ideas not previously available in English and will be of interest to graduate students and professionals in mathematics and probability theory.

Combinatorial Geometries

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521333399

Category: Mathematics

Page: 212

View: 7242

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This book is a continuation of Theory of Matroids and again consists of a series of related surveys.

Robust Algebraic Multilevel Methods and Algorithms

Author: Johannes Kraus,Svetozar Margenov

Publisher: Walter de Gruyter

ISBN: 3110214830

Category: Mathematics

Page: 256

View: 1172

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This book deals with algorithms for the solution of linear systems of algebraic equations with large-scale sparse matrices, with a focus on problems that are obtained after discretization of partial differential equations using finite element methods. Provides a systematic presentation of the recent advances in robust algebraic multilevel methods. Can be used for advanced courses on the topic.