Combinatorial And Graph Theoretical Problems In Linear Algebra

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Combinatorial and Graph-Theoretical Problems in Linear Algebra

Author : Richard A. Brualdi
Publisher : Springer Science & Business Media
ISBN 13 : 1461383544
Total Pages : 266 pages
Book Rating : 4.4/5 (613 download)

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Book Synopsis Combinatorial and Graph-Theoretical Problems in Linear Algebra by : Richard A. Brualdi

Download or read book Combinatorial and Graph-Theoretical Problems in Linear Algebra written by Richard A. Brualdi and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt: This IMA Volume in Mathematics and its Applications COMBINATORIAL AND GRAPH-THEORETICAL PROBLEMS IN LINEAR ALGEBRA is based on the proceedings of a workshop that was an integral part of the 1991-92 IMA program on "Applied Linear Algebra." We are grateful to Richard Brualdi, George Cybenko, Alan George, Gene Golub, Mitchell Luskin, and Paul Van Dooren for planning and implementing the year-long program. We especially thank Richard Brualdi, Shmuel Friedland, and Victor Klee for organizing this workshop and editing the proceedings. The financial support of the National Science Foundation made the workshop possible. A vner Friedman Willard Miller, Jr. PREFACE The 1991-1992 program of the Institute for Mathematics and its Applications (IMA) was Applied Linear Algebra. As part of this program, a workshop on Com binatorial and Graph-theoretical Problems in Linear Algebra was held on November 11-15, 1991. The purpose of the workshop was to bring together in an informal setting the diverse group of people who work on problems in linear algebra and matrix theory in which combinatorial or graph~theoretic analysis is a major com ponent. Many of the participants of the workshop enjoyed the hospitality of the IMA for the entire fall quarter, in which the emphasis was discrete matrix analysis.

Combinatorial and Graph-theoretical Problems in Linear Algebra

Author : Richard A. Brualdi
Publisher :
ISBN 13 : 9783540940869
Total Pages : 260 pages
Book Rating : 4.9/5 (48 download)

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Book Synopsis Combinatorial and Graph-theoretical Problems in Linear Algebra by : Richard A. Brualdi

Download or read book Combinatorial and Graph-theoretical Problems in Linear Algebra written by Richard A. Brualdi and published by . This book was released on 1993-01-01 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Matrices in Combinatorics and Graph Theory

Author : Bolian Liu
Publisher : Springer Science & Business Media
ISBN 13 : 1475731655
Total Pages : 317 pages
Book Rating : 4.4/5 (757 download)

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Book Synopsis Matrices in Combinatorics and Graph Theory by : Bolian Liu

Download or read book Matrices in Combinatorics and Graph Theory written by Bolian Liu and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 317 pages. Available in PDF, EPUB and Kindle. Book excerpt: Combinatorics and Matrix Theory have a symbiotic, or mutually beneficial, relationship. This relationship is discussed in my paper The symbiotic relationship of combinatorics and matrix theoryl where I attempted to justify this description. One could say that a more detailed justification was given in my book with H. J. Ryser entitled Combinatorial Matrix Theon? where an attempt was made to give a broad picture of the use of combinatorial ideas in matrix theory and the use of matrix theory in proving theorems which, at least on the surface, are combinatorial in nature. In the book by Liu and Lai, this picture is enlarged and expanded to include recent developments and contributions of Chinese mathematicians, many of which have not been readily available to those of us who are unfamiliar with Chinese journals. Necessarily, there is some overlap with the book Combinatorial Matrix Theory. Some of the additional topics include: spectra of graphs, eulerian graph problems, Shannon capacity, generalized inverses of Boolean matrices, matrix rearrangements, and matrix completions. A topic to which many Chinese mathematicians have made substantial contributions is the combinatorial analysis of powers of nonnegative matrices, and a large chapter is devoted to this topic. This book should be a valuable resource for mathematicians working in the area of combinatorial matrix theory. Richard A. Brualdi University of Wisconsin - Madison 1 Linear Alg. Applies., vols. 162-4, 1992, 65-105 2Camhridge University Press, 1991.

Combinatorial Matrix Theory

Author : Richard A. Brualdi
Publisher : Birkhäuser
ISBN 13 : 3319709534
Total Pages : 228 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Combinatorial Matrix Theory by : Richard A. Brualdi

Download or read book Combinatorial Matrix Theory written by Richard A. Brualdi and published by Birkhäuser. This book was released on 2018-03-31 with total page 228 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

50 years of Combinatorics, Graph Theory, and Computing

Author : Fan Chung
Publisher : CRC Press
ISBN 13 : 100075183X
Total Pages : 443 pages
Book Rating : 4.0/5 (7 download)

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Book Synopsis 50 years of Combinatorics, Graph Theory, and Computing by : Fan Chung

Download or read book 50 years of Combinatorics, Graph Theory, and Computing written by Fan Chung and published by CRC Press. This book was released on 2019-11-15 with total page 443 pages. Available in PDF, EPUB and Kindle. Book excerpt: 50 Years of Combinatorics, Graph Theory, and Computing advances research in discrete mathematics by providing current research surveys, each written by experts in their subjects. The book also celebrates outstanding mathematics from 50 years at the Southeastern International Conference on Combinatorics, Graph Theory & Computing (SEICCGTC). The conference is noted for the dissemination and stimulation of research, while fostering collaborations among mathematical scientists at all stages of their careers. The authors of the chapters highlight open questions. The sections of the book include: Combinatorics; Graph Theory; Combinatorial Matrix Theory; Designs, Geometry, Packing and Covering. Readers will discover the breadth and depth of the presentations at the SEICCGTC, as well as current research in combinatorics, graph theory and computer science. Features: Commemorates 50 years of the Southeastern International Conference on Combinatorics, Graph Theory & Computing with research surveys Surveys highlight open questions to inspire further research Chapters are written by experts in their fields Extensive bibliographies are provided at the end of each chapter

Locating Eigenvalues in Graphs

Author : Carlos Hoppen
Publisher : Springer Nature
ISBN 13 : 3031116984
Total Pages : 142 pages
Book Rating : 4.0/5 (311 download)

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Book Synopsis Locating Eigenvalues in Graphs by : Carlos Hoppen

Download or read book Locating Eigenvalues in Graphs written by Carlos Hoppen and published by Springer Nature. This book was released on 2022-09-21 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book focuses on linear time eigenvalue location algorithms for graphs. This subject relates to spectral graph theory, a field that combines tools and concepts of linear algebra and combinatorics, with applications ranging from image processing and data analysis to molecular descriptors and random walks. It has attracted a lot of attention and has since emerged as an area on its own. Studies in spectral graph theory seek to determine properties of a graph through matrices associated with it. It turns out that eigenvalues and eigenvectors have surprisingly many connections with the structure of a graph. This book approaches this subject under the perspective of eigenvalue location algorithms. These are algorithms that, given a symmetric graph matrix M and a real interval I, return the number of eigenvalues of M that lie in I. Since the algorithms described here are typically very fast, they allow one to quickly approximate the value of any eigenvalue, which is a basic step in most applications of spectral graph theory. Moreover, these algorithms are convenient theoretical tools for proving bounds on eigenvalues and their multiplicities, which was quite useful to solve longstanding open problems in the area. This book brings these algorithms together, revealing how similar they are in spirit, and presents some of their main applications. This work can be of special interest to graduate students and researchers in spectral graph theory, and to any mathematician who wishes to know more about eigenvalues associated with graphs. It can also serve as a compact textbook for short courses on the topic.

Eigenspaces of Graphs

Author : Dragoš M. Cvetković
Publisher : Cambridge University Press
ISBN 13 : 0521573521
Total Pages : 284 pages
Book Rating : 4.5/5 (215 download)

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Book Synopsis Eigenspaces of Graphs by : Dragoš M. Cvetković

Download or read book Eigenspaces of Graphs written by Dragoš M. Cvetković and published by Cambridge University Press. This book was released on 1997-01-09 with total page 284 pages. Available in PDF, EPUB and Kindle. Book excerpt: Current research on the spectral theory of finite graphs may be seen as part of a wider effort to forge closer links between algebra and combinatorics (in particular between linear algebra and graph theory).This book describes how this topic can be strengthened by exploiting properties of the eigenspaces of adjacency matrices associated with a graph. The extension of spectral techniques proceeds at three levels: using eigenvectors associated with an arbitrary labelling of graph vertices, using geometrical invariants of eigenspaces such as graph angles and main angles, and introducing certain kinds of canonical eigenvectors by means of star partitions and star bases. One objective is to describe graphs by algebraic means as far as possible, and the book discusses the Ulam reconstruction conjecture and the graph isomorphism problem in this context. Further problems of graph reconstruction and identification are used to illustrate the importance of graph angles and star partitions in relation to graph structure. Specialists in graph theory will welcome this treatment of important new research.

Advanced Graph Theory and Combinatorics

Author : Michel Rigo
Publisher : John Wiley & Sons
ISBN 13 : 1119058643
Total Pages : 237 pages
Book Rating : 4.1/5 (19 download)

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Book Synopsis Advanced Graph Theory and Combinatorics by : Michel Rigo

Download or read book Advanced Graph Theory and Combinatorics written by Michel Rigo and published by John Wiley & Sons. This book was released on 2016-11-22 with total page 237 pages. Available in PDF, EPUB and Kindle. Book excerpt: Advanced Graph Theory focuses on some of the main notions arising in graph theory with an emphasis from the very start of the book on the possible applications of the theory and the fruitful links existing with linear algebra. The second part of the book covers basic material related to linear recurrence relations with application to counting and the asymptotic estimate of the rate of growth of a sequence satisfying a recurrence relation.

Graph Algorithms in the Language of Linear Algebra

Author : Jeremy Kepner
Publisher : SIAM
ISBN 13 : 9780898719918
Total Pages : 388 pages
Book Rating : 4.7/5 (199 download)

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Book Synopsis Graph Algorithms in the Language of Linear Algebra by : Jeremy Kepner

Download or read book Graph Algorithms in the Language of Linear Algebra written by Jeremy Kepner and published by SIAM. This book was released on 2011-01-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: The current exponential growth in graph data has forced a shift to parallel computing for executing graph algorithms. Implementing parallel graph algorithms and achieving good parallel performance have proven difficult. This book addresses these challenges by exploiting the well-known duality between a canonical representation of graphs as abstract collections of vertices and edges and a sparse adjacency matrix representation. This linear algebraic approach is widely accessible to scientists and engineers who may not be formally trained in computer science. The authors show how to leverage existing parallel matrix computation techniques and the large amount of software infrastructure that exists for these computations to implement efficient and scalable parallel graph algorithms. The benefits of this approach are reduced algorithmic complexity, ease of implementation, and improved performance.

A First Course in Graph Theory and Combinatorics

Author : Sebastian M. Cioabă
Publisher : Springer
ISBN 13 : 9386279398
Total Pages : 186 pages
Book Rating : 4.3/5 (862 download)

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Book Synopsis A First Course in Graph Theory and Combinatorics by : Sebastian M. Cioabă

Download or read book A First Course in Graph Theory and Combinatorics written by Sebastian M. Cioabă and published by Springer. This book was released on 2009-05-15 with total page 186 pages. Available in PDF, EPUB and Kindle. Book excerpt: The concept of a graph is fundamental in mathematics since it conveniently encodes diverse relations and facilitates combinatorial analysis of many complicated counting problems. In this book, the authors have traced the origins of graph theory from its humble beginnings of recreational mathematics to its modern setting for modeling communication networks as is evidenced by the World Wide Web graph used by many Internet search engines. This book is an introduction to graph theory and combinatorial analysis. It is based on courses given by the second author at Queen's University at Kingston, Ontario, Canada between 2002 and 2008. The courses were aimed at students in their final year of their undergraduate program.

Graph Theory and Additive Combinatorics

Author : Yufei Zhao
Publisher : Cambridge University Press
ISBN 13 : 1009310933
Total Pages : 336 pages
Book Rating : 4.0/5 (93 download)

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Book Synopsis Graph Theory and Additive Combinatorics by : Yufei Zhao

Download or read book Graph Theory and Additive Combinatorics written by Yufei Zhao and published by Cambridge University Press. This book was released on 2023-07-31 with total page 336 pages. Available in PDF, EPUB and Kindle. Book excerpt: Using the dichotomy of structure and pseudorandomness as a central theme, this accessible text provides a modern introduction to extremal graph theory and additive combinatorics. Readers will explore central results in additive combinatorics-notably the cornerstone theorems of Roth, Szemerédi, Freiman, and Green-Tao-and will gain additional insights into these ideas through graph theoretic perspectives. Topics discussed include the Turán problem, Szemerédi's graph regularity method, pseudorandom graphs, graph limits, graph homomorphism inequalities, Fourier analysis in additive combinatorics, the structure of set addition, and the sum-product problem. Important combinatorial, graph theoretic, analytic, Fourier, algebraic, and geometric methods are highlighted. Students will appreciate the chapter summaries, many figures and exercises, and freely available lecture videos on MIT OpenCourseWare. Meant as an introduction for students and researchers studying combinatorics, theoretical computer science, analysis, probability, and number theory, the text assumes only basic familiarity with abstract algebra, analysis, and linear algebra.

Combinatorial Mathematics

Author : D. Bresson
Publisher : Elsevier
ISBN 13 : 0080871860
Total Pages : 683 pages
Book Rating : 4.0/5 (88 download)

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Book Synopsis Combinatorial Mathematics by : D. Bresson

Download or read book Combinatorial Mathematics written by D. Bresson and published by Elsevier. This book was released on 2012-01-25 with total page 683 pages. Available in PDF, EPUB and Kindle. Book excerpt: The object of this book is to provide an account of the results and methods used in combinatorial theories: Graph Theory, Matching Theory, Hamiltonian Problems, Hypergraph Theory, Designs, Steiner Systems, Latin Squares, Coding Matroids, Complexity Theory. In publishing this volume, the editors do not intend to discuss all the classical open problems in combinatorics for which an algebraic approach turns out to be useful. The work is a selection which is intended for specialists, as well as for graduate students who may also be interested in survey papers. The work features a special section which contains a list of unsolved problems proposed by the participants.

Topics in Algebraic Graph Theory

Author : Lowell W. Beineke
Publisher : Cambridge University Press
ISBN 13 : 1107079454
Total Pages : 302 pages
Book Rating : 4.1/5 (7 download)

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Book Synopsis Topics in Algebraic Graph Theory by : Lowell W. Beineke

Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: The rapidly expanding area of algebraic graph theory uses two different branches of algebra to explore various aspects of graph theory: linear algebra (for spectral theory) and group theory (for studying graph symmetry). These areas have links with other areas of mathematics, such as logic and harmonic analysis, and are increasingly being used in such areas as computer networks where symmetry is an important feature. Other books cover portions of this material, but this book is unusual in covering both of these aspects and there are no other books with such a wide scope. Peter J. Cameron, internationally recognized for his substantial contributions to the area, served as academic consultant for this volume, and the result is ten 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, linear algebra and group theory. Each chapter concludes with an extensive list of references.

Inverse Problems and Zero Forcing for Graphs

Author : Leslie Hogben
Publisher : American Mathematical Society
ISBN 13 : 1470466554
Total Pages : 302 pages
Book Rating : 4.4/5 (74 download)

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Book Synopsis Inverse Problems and Zero Forcing for Graphs by : Leslie Hogben

Download or read book Inverse Problems and Zero Forcing for Graphs written by Leslie Hogben and published by American Mathematical Society. This book was released on 2022-07-21 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an introduction to the inverse eigenvalue problem for graphs (IEP-$G$) and the related area of zero forcing, propagation, and throttling. The IEP-$G$ grew from the intersection of linear algebra and combinatorics and has given rise to both a rich set of deep problems in that area as well as a breadth of “ancillary” problems in related areas. The IEP-$G$ asks a fundamental mathematical question expressed in terms of linear algebra and graph theory, but the significance of such questions goes beyond these two areas, as particular instances of the IEP-$G$ also appear as major research problems in other fields of mathematics, sciences and engineering. One approach to the IEP-$G$ is through rank minimization, a relevant problem in itself and with a large number of applications. During the past 10 years, important developments on the rank minimization problem, particularly in relation to zero forcing, have led to significant advances in the IEP-$G$. The monograph serves as an entry point and valuable resource that will stimulate future developments in this active and mathematically diverse research area.

Graph Theory, Combinatorics and Algorithms

Author : Martin Charles Golumbic
Publisher : Springer Science & Business Media
ISBN 13 : 0387250360
Total Pages : 296 pages
Book Rating : 4.3/5 (872 download)

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Book Synopsis Graph Theory, Combinatorics and Algorithms by : Martin Charles Golumbic

Download or read book Graph Theory, Combinatorics and Algorithms written by Martin Charles Golumbic and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 296 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory, Combinatorics and Algorithms: Interdisciplinary Applications focuses on discrete mathematics and combinatorial algorithms interacting with real world problems in computer science, operations research, applied mathematics and engineering. The book contains eleven chapters written by experts in their respective fields, and covers a wide spectrum of high-interest problems across these discipline domains. Among the contributing authors are Richard Karp of UC Berkeley and Robert Tarjan of Princeton; both are at the pinnacle of research scholarship in Graph Theory and Combinatorics. The chapters from the contributing authors focus on "real world" applications, all of which will be of considerable interest across the areas of Operations Research, Computer Science, Applied Mathematics, and Engineering. These problems include Internet congestion control, high-speed communication networks, multi-object auctions, resource allocation, software testing, data structures, etc. In sum, this is a book focused on major, contemporary problems, written by the top research scholars in the field, using cutting-edge mathematical and computational techniques.

Applications of Group Theory to Combinatorics

Author : Jack Koolen
Publisher : CRC Press
ISBN 13 : 0203885767
Total Pages : 188 pages
Book Rating : 4.2/5 (38 download)

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Book Synopsis Applications of Group Theory to Combinatorics by : Jack Koolen

Download or read book Applications of Group Theory to Combinatorics written by Jack Koolen and published by CRC Press. This book was released on 2008-07-02 with total page 188 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applications of Group Theory to Combinatorics contains 11 survey papers from international experts in combinatorics, group theory and combinatorial topology. The contributions cover topics from quite a diverse spectrum, such as design theory, Belyi functions, group theory, transitive graphs, regular maps, and Hurwitz problems, and present the state

A Course in Combinatorics

Author : J. H. van Lint
Publisher : Cambridge University Press
ISBN 13 : 9780521006019
Total Pages : 620 pages
Book Rating : 4.0/5 (6 download)

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Book Synopsis A Course in Combinatorics by : J. H. van Lint

Download or read book A Course in Combinatorics written by J. H. van Lint and published by Cambridge University Press. This book was released on 2001-11-22 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the second edition of a popular book on combinatorics, a subject dealing with ways of arranging and distributing objects, and which involves ideas from geometry, algebra and analysis. The breadth of the theory is matched by that of its applications, which include topics as diverse as codes, circuit design and algorithm complexity. It has thus become essential for workers in many scientific fields to have some familiarity with the subject. The authors have tried to be as comprehensive as possible, dealing in a unified manner with, for example, graph theory, extremal problems, designs, colorings and codes. The depth and breadth of the coverage make the book a unique guide to the whole of the subject. The book is ideal for courses on combinatorical mathematics at the advanced undergraduate or beginning graduate level. Working mathematicians and scientists will also find it a valuable introduction and reference.