Eigenspaces of Graphs

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

Publisher: Cambridge University Press

ISBN: 9780521573528

Category: Mathematics

Page: 258

View: 1926

This book describes the spectral theory of finite graphs.

Matroid Applications

Author: Neil White

Publisher: Cambridge University Press

ISBN: 9780521381659

Category: Mathematics

Page: 363

View: 2813

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).


Author: Henryk Minc

Publisher: Cambridge University Press

ISBN: 9780521302265

Category: Mathematics

Page: 224

View: 9501

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.

Relational Mathematics

Author: Gunther Schmidt

Publisher: Cambridge University Press

ISBN: 0521762685

Category: Computers

Page: 567

View: 5137

A modern, comprehensive 2010 overview providing an easy introduction for applied scientists who are not versed in mathematics.

Topics in Algebraic Graph Theory

Author: Lowell W. Beineke,Robin J. Wilson

Publisher: Cambridge University Press

ISBN: 9780521801973

Category: Mathematics

Page: 276

View: 4225

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

The Mutually Beneficial Relationship of Graphs and Matrices

Author: Richard A. Brualdi

Publisher: American Mathematical Soc.

ISBN: 0821853155

Category: Mathematics

Page: 96

View: 8207

Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.

Eigenvalues, Multiplicities and Graphs

Author: Charles R. Johnson,Carlos M. Saiago

Publisher: Cambridge University Press

ISBN: 1108547036

Category: Mathematics

Page: N.A

View: 1276

The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

Model Theory

Author: Wilfrid Hodges

Publisher: Cambridge University Press

ISBN: 9780521304429

Category: Mathematics

Page: 772

View: 4318

Model theory is concerned with the notions of definition, interpretation and structure in a very general setting, and is applied to a wide range of other areas such as set theory, geometry, algebra and computer science. This book provides an integrated introduction to model theory for graduate students.

Combinatorial Matrix Theory

Author: Richard A. Brualdi,Ángeles Carmona,P. van den Driessche,Stephen Kirkland,Dragan Stevanović

Publisher: Birkhäuser

ISBN: 3319709534

Category: Mathematics

Page: 219

View: 4521

This book contains the notes of the lectures delivered at an Advanced Course on Combinatorial Matrix Theory held at Centre de Recerca Matemàtica (CRM) in Barcelona. These notes correspond to five series of lectures. The first series is dedicated to the study of several matrix classes defined combinatorially, and was delivered by Richard A. Brualdi. The second one, given by Pauline van den Driessche, is concerned with the study of spectral properties of matrices with a given sign pattern. Dragan Stevanović delivered the third one, devoted to describing the spectral radius of a graph as a tool to provide bounds of parameters related with properties of a graph. The fourth lecture was delivered by Stephen Kirkland and is dedicated to the applications of the Group Inverse of the Laplacian matrix. The last one, given by Ángeles Carmona, focuses on boundary value problems on finite networks with special in-depth on the M-matrix inverse problem.

Nonnegative Matrices and Applications

Author: R. B. Bapat,T. E. S. Raghavan

Publisher: Cambridge University Press

ISBN: 9780521571678

Category: Mathematics

Page: 336

View: 317

This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

Graph Theory and Its Applications, Second Edition

Author: Jonathan L. Gross,Jay Yellen

Publisher: CRC Press

ISBN: 158488505X

Category: Mathematics

Page: 800

View: 9858

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.

Surveys in Combinatorics

Invited Papers for the ... British Combinatorial Conference

Author: Anthony Hilton,John Talbot

Publisher: N.A


Category: Combinatorial analysis

Page: N.A

View: 5478

Mathematics of Bioinformatics

Theory, Methods and Applications

Author: Matthew He,Sergey Petoukhov

Publisher: John Wiley & Sons

ISBN: 9781118099520

Category: Computers

Page: 298

View: 7740

Mathematics of Bioinformatics: Theory, Methods, and Applications provides a comprehensive format for connecting and integrating information derived from mathematical methods and applying it to the understanding of biological sequences, structures, and networks. Each chapter is divided into a number of sections based on the bioinformatics topics and related mathematical theory and methods. Each topic of the section is comprised of the following three parts: an introduction to the biological problems in bioinformatics; a presentation of relevant topics of mathematical theory and methods to the bioinformatics problems introduced in the first part; an integrative overview that draws the connections and interfaces between bioinformatics problems/issues and mathematical theory/methods/applications.

Bipartite Graphs and Their Applications

Author: Armen S. Asratian,Tristan M. J. Denley,Roland Häggkvist

Publisher: Cambridge University Press

ISBN: 9780521593458

Category: Mathematics

Page: 259

View: 9964

This book treats the fundamental mathematical properties that hold for a family of Gaussian random variables.

Polynomials with Special Regard to Reducibility

Author: A. Schinzel

Publisher: Cambridge University Press

ISBN: 9781139426718

Category: Mathematics

Page: N.A

View: 3322

This book covers most of the known results on reducibility of polynomials over arbitrary fields, algebraically closed fields and finitely generated fields. Results valid only over finite fields, local fields or the rational field are not covered here, but several theorems on reducibility of polynomials over number fields that are either totally real or complex multiplication fields are included. Some of these results are based on recent work of E. Bombieri and U. Zannier (presented here by Zannier in an appendix). The book also treats other subjects like Ritt's theory of composition of polynomials, and properties of the Mahler measure, and it concludes with a bibliography of over 300 items. This unique work will be a necessary resource for all number theorists and researchers in related fields.

Ars Combinatoria

Author: N.A

Publisher: N.A


Category: Combinatorial analysis

Page: N.A

View: 1977

A First Course in Network Theory

Author: Ernesto Estrada,Philip Knight

Publisher: Oxford University Press, USA

ISBN: 0198726457

Category: Electronic books

Page: 254

View: 3626

The study of network theory is a highly interdisciplinary field, which has emerged as a major topic of interest in various disciplines ranging from physics and mathematics, to biology and sociology. This book promotes the diverse nature of the study of complex networks by balancing the needs of students from very different backgrounds. It references the most commonly used concepts in network theory, provides examples of their applications in solving practical problems, and clear indications on how to analyse their results. In the first part of the book, students and researchers will discover the quantitative and analytical tools necessary to work with complex networks, including the most basic concepts in network and graph theory, linear and matrix algebra, as well as the physical concepts most frequently used for studying networks. They will also find instruction on some key skills such as how to proof analytic results and how to manipulate empirical network data. The bulk of the text is focused on instructing readers on the most useful tools for modern practitioners of network theory. These include degree distributions, random networks, network fragments, centrality measures, clusters and communities, communicability, and local and global properties of networks. The combination of theory, example and method that are presented in this text, should ready the student to conduct their own analysis of networks with confidence and allow teachers to select appropriate examples and problems to teach this subject in the classroom.

Mathematical Theory of Entropy

Author: Nathaniel F. G. Martin,James W. England

Publisher: Cambridge University Press

ISBN: 9780521177382

Category: Mathematics

Page: 286

View: 6173

This excellent 1981 treatment of the mathematical theory of entropy gives an accessible exposition its application to other fields.