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Matrices In Combinatorics And Graph Theory
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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.
Book Synopsis Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs by : Jason J. Molitierno
Download or read book Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs written by Jason J. Molitierno and published by CRC Press. This book was released on 2016-04-19 with total page 425 pages. Available in PDF, EPUB and Kindle. Book excerpt: On the surface, matrix theory and graph theory seem like very different branches of mathematics. However, adjacency, Laplacian, and incidence matrices are commonly used to represent graphs, and many properties of matrices can give us useful information about the structure of graphs.Applications of Combinatorial Matrix Theory to Laplacian Matrices o
Book Synopsis Combinatorics and Graph Theory by : John Harris
Download or read book Combinatorics and Graph Theory written by John Harris and published by Springer Science & Business Media. This book was released on 2009-04-03 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: These notes were first used in an introductory course team taught by the authors at Appalachian State University to advanced undergraduates and beginning graduates. The text was written with four pedagogical goals in mind: offer a variety of topics in one course, get to the main themes and tools as efficiently as possible, show the relationships between the different topics, and include recent results to convince students that mathematics is a living discipline.
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 . This book was released on 2014-09-01 with total page 324 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis A Combinatorial Approach to Matrix Theory and Its Applications by : Richard A. Brualdi
Download or read book A Combinatorial Approach to Matrix Theory and Its Applications written by Richard A. Brualdi and published by CRC Press. This book was released on 2008-08-06 with total page 288 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unlike most elementary books on matrices, A Combinatorial Approach to Matrix Theory and Its Applications employs combinatorial and graph-theoretical tools to develop basic theorems of matrix theory, shedding new light on the subject by exploring the connections of these tools to matrices. After reviewing the basics of graph theory, elementary counting formulas, fields, and vector spaces, the book explains the algebra of matrices and uses the König digraph to carry out simple matrix operations. It then discusses matrix powers, provides a graph-theoretical definition of the determinant using the Coates digraph of a matrix, and presents a graph-theoretical interpretation of matrix inverses. The authors develop the elementary theory of solutions of systems of linear equations and show how to use the Coates digraph to solve a linear system. They also explore the eigenvalues, eigenvectors, and characteristic polynomial of a matrix; examine the important properties of nonnegative matrices that are part of the Perron–Frobenius theory; and study eigenvalue inclusion regions and sign-nonsingular matrices. The final chapter presents applications to electrical engineering, physics, and chemistry. Using combinatorial and graph-theoretical tools, this book enables a solid understanding of the fundamentals of matrix theory and its application to scientific areas.
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 219 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.
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
Book Synopsis Combinatorial Matrix Theory and Generalized Inverses of Matrices by : Ravindra B. Bapat
Download or read book Combinatorial Matrix Theory and Generalized Inverses of Matrices written by Ravindra B. Bapat and published by Springer Science & Business Media. This book was released on 2013-02-11 with total page 283 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book consists of eighteen articles in the area of `Combinatorial Matrix Theory' and `Generalized Inverses of Matrices'. Original research and expository articles presented in this publication are written by leading Mathematicians and Statisticians working in these areas. The articles contained herein are on the following general topics: `matrices in graph theory', `generalized inverses of matrices', `matrix methods in statistics' and `magic squares'. In the area of matrices and graphs, speci_c topics addressed in this volume include energy of graphs, q-analog, immanants of matrices and graph realization of product of adjacency matrices. Topics in the book from `Matrix Methods in Statistics' are, for example, the analysis of BLUE via eigenvalues of covariance matrix, copulas, error orthogonal model, and orthogonal projectors in the linear regression models. Moore-Penrose inverse of perturbed operators, reverse order law in the case of inde_nite inner product space, approximation numbers, condition numbers, idempotent matrices, semiring of nonnegative matrices, regular matrices over incline and partial order of matrices are the topics addressed under the area of theory of generalized inverses. In addition to the above traditional topics and a report on CMTGIM 2012 as an appendix, we have an article on old magic squares from India.
Book Synopsis Combinatorial Matrix Classes by : Richard A. Brualdi
Download or read book Combinatorial Matrix Classes written by Richard A. Brualdi and published by Cambridge University Press. This book was released on 2006-08-10 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Graph Theory and Sparse Matrix Computation by : Alan George
Download or read book Graph Theory and Sparse Matrix Computation written by Alan George and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: When reality is modeled by computation, matrices are often the connection between the continuous physical world and the finite algorithmic one. Usually, the more detailed the model, the bigger the matrix, the better the answer, however, efficiency demands that every possible advantage be exploited. The articles in this volume are based on recent research on sparse matrix computations. This volume looks at graph theory as it connects to linear algebra, parallel computing, data structures, geometry, and both numerical and discrete algorithms. The articles are grouped into three general categories: graph models of symmetric matrices and factorizations, graph models of algorithms on nonsymmetric matrices, and parallel sparse matrix algorithms. This book will be a resource for the researcher or advanced student of either graphs or sparse matrices; it will be useful to mathematicians, numerical analysts and theoretical computer scientists alike.
Book Synopsis Graphs, Matrices, and Designs by : Rolf S. Rees
Download or read book Graphs, Matrices, and Designs written by Rolf S. Rees and published by Routledge. This book was released on 2017-07-12 with total page 339 pages. Available in PDF, EPUB and Kindle. Book excerpt: Examines partitions and covers of graphs and digraphs, latin squares, pairwise balanced designs with prescribed block sizes, ranks and permanents, extremal graph theory, Hadamard matrices and graph factorizations. This book is designed to be of interest to applied mathematicians, computer scientists and communications researchers.
Book Synopsis Graphs and Matrices by : Ravindra B. Bapat
Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Graph Theory written by B Andrasfai and published by CRC Press. This book was released on 1991-01-01 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt: Graph Theory: Flows, Matrices covers a number of topics in graph theory that are important in the major areas of application. It provides graph theoretic tools that can be readily and efficiently applied to problems in operational research, computer science, electrical engineering, and economics. Emphasizing didactic principles, the book derives theorems and proofs from a detailed analysis of the structure of graphs. The easy-to-follow algorithms can be readily converted to computer codes in high-level programming languages. Requiring knowledge of the basic concepts of graph theory and a familiarity with some simple results, the book also includes 100 exercises with solutions to help readers gain experience and 131 diagrams to aid in the understanding of concepts and proofs.
Book Synopsis The Mutually Beneficial Relationship of Graphs and Matrices by : Richard A. Brualdi
Download or read book The Mutually Beneficial Relationship of Graphs and Matrices written by Richard A. Brualdi and published by American Mathematical Soc.. This book was released on 2011-07-06 with total page 110 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Matrix Inequalities for Iterative Systems by : Hanjo Taubig
Download or read book Matrix Inequalities for Iterative Systems written by Hanjo Taubig and published by CRC Press. This book was released on 2017-02-03 with total page 219 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book reviews inequalities for weighted entry sums of matrix powers. Applications range from mathematics and CS to pure sciences. It unifies and generalizes several results for products and powers of sesquilinear forms derived from powers of Hermitian, positive-semidefinite, as well as nonnegative matrices. It shows that some inequalities are valid only in specific cases. How to translate the Hermitian matrix results into results for alternating powers of general rectangular matrices? Inequalities that compare the powers of the row and column sums to the row and column sums of the matrix powers are refined for nonnegative matrices. Lastly, eigenvalue bounds and derive results for iterated kernels are improved.
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 Nature. This book was released on 2022-07-07 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the origin of graph theory from its humble beginnings in recreational mathematics to its modern setting or modeling communication networks, as is evidenced by the World Wide Web graph used by many Internet search engines. The second edition of the book includes recent developments in the theory of signed adjacency matrices involving the proof of sensitivity conjecture and the theory of Ramanujan graphs. In addition, the book discusses topics such as Pick’s theorem on areas of lattice polygons and Graham–Pollak’s work on addressing of graphs. The concept of graph is fundamental in mathematics and engineering, as it conveniently encodes diverse relations and facilitates combinatorial analysis of many theoretical and practical problems. The text is ideal for a one-semester course at the advanced undergraduate level or beginning graduate level.
Book Synopsis Matrices and Matroids for Systems Analysis by : Kazuo Murota
Download or read book Matrices and Matroids for Systems Analysis written by Kazuo Murota and published by Springer Science & Business Media. This book was released on 1999-11-29 with total page 500 pages. Available in PDF, EPUB and Kindle. Book excerpt: A matroid is an abstract mathematical structure that captures combinatorial properties of matrices. This book offers a unique introduction to matroid theory, emphasizing motivations from matrix theory and applications to systems analysis. This book serves also as a comprehensive presentation of the theory and application of mixed matrices, developed primarily by the present author in the 1990's. A mixed matrix is a convenient mathematical tool for systems analysis, compatible with the physical observation that "fixed constants" and "system parameters" are to be distinguished in the description of engineering systems. This book will be extremely useful to graduate students and researchers in engineering, mathematics and computer science. From the reviews: "...The book has been prepared very carefully, contains a lot of interesting results and is highly recommended for graduate and postgraduate students." András Recski, Mathematical Reviews Clippings 2000m:93006
