Graphs And Matrices

Author : Ravindra B. Bapat
Publisher : Springer
Page : 193 pages
File Size : 45,6 Mb
Release : 2014-09-19
Category : Mathematics
ISBN : 9781447165699

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Graphs and Matrices by Ravindra B. Bapat Pdf

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.

Author : Richard A. Brualdi
Publisher : American Mathematical Soc.
Page : 110 pages
File Size : 54,6 Mb
Release : 2011-07-06
Category : Mathematics
ISBN : 9780821853153

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The Mutually Beneficial Relationship of Graphs and Matrices by Richard A. Brualdi Pdf

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.

Author : Rolf S. Rees
Publisher : Routledge
Page : 339 pages
File Size : 50,6 Mb
Release : 2017-07-12
Category : Mathematics
ISBN : 9781351444385

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Graphs, Matrices, and Designs by Rolf S. Rees Pdf

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.

Author : Ravindra B. Bapat
Publisher : Springer Science & Business Media
Page : 171 pages
File Size : 53,5 Mb
Release : 2010-07-23
Category : Mathematics
ISBN : 9781848829817

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Graphs and Matrices by Ravindra B. Bapat Pdf

Graphs and Matrices provides a welcome addition to the rapidly expanding selection of literature in this field. As the title suggests, the book’s primary focus is graph theory, with an emphasis on topics relating to linear algebra and matrix theory. Information is presented at a relatively elementary level with the view of leading the student into further research. In the first part of the book matrix preliminaries are discussed and the basic properties of graph-associated matrices highlighted. Further topics include those of graph theory such as regular graphs and algebraic connectivity, Laplacian eigenvalues of threshold graphs, positive definite completion problem and graph-based matrix games. Whilst this book will be invaluable to researchers in graph theory, it may also be of benefit to a wider, cross-disciplinary readership.

Author : Jason J. Molitierno
Publisher : CRC Press
Page : 425 pages
File Size : 41,7 Mb
Release : 2016-04-19
Category : Computers
ISBN : 9781439863398

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Applications of Combinatorial Matrix Theory to Laplacian Matrices of Graphs by Jason J. Molitierno Pdf

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

Author : Miroslav Fiedler
Publisher : Cambridge University Press
Page : 206 pages
File Size : 51,7 Mb
Release : 2011-02-03
Category : Mathematics
ISBN : 9780521461931

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Matrices and Graphs in Geometry by Miroslav Fiedler Pdf

Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.

Author : Bolian Liu,Hong-Jian Lai
Publisher : Springer Science & Business Media
Page : 317 pages
File Size : 55,9 Mb
Release : 2013-03-09
Category : Mathematics
ISBN : 9781475731651

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Matrices in Combinatorics and Graph Theory by Bolian Liu,Hong-Jian Lai Pdf

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.

Author : D. Logofet
Publisher : CRC Press
Page : 388 pages
File Size : 54,7 Mb
Release : 2018-02-01
Category : Science
ISBN : 9781351091220

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Matrices and Graphs Stability Problems in Mathematical Ecology by D. Logofet Pdf

Intuitive ideas of stability in dynamics of a biological population, community, or ecosystem can be formalized in the framework of corresponding mathematical models. These are often represented by systems of ordinary differential equations or difference equations. Matrices and Graphs covers achievements in the field using concepts from matrix theory and graph theory. The book effectively surveys applications of mathematical results pertinent to issues of theoretical and applied ecology. The only mathematical prerequisite for using Matrices and Graphs is a working knowledge of linear algebra and matrices. The book is ideal for biomathematicians, ecologists, and applied mathematicians doing research on dynamic behavior of model populations and communities consisting of multi-component systems. It will also be valuable as a text for a graduate-level topics course in applied math or mathematical ecology.

Author : Alan George,John R. Gilbert,Joseph W.H. Liu
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 51,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461383697

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Graph Theory and Sparse Matrix Computation by Alan George,John R. Gilbert,Joseph W.H. Liu Pdf

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.

Author : B Andrasfai
Publisher : CRC Press
Page : 298 pages
File Size : 48,8 Mb
Release : 1991-01-01
Category : Mathematics
ISBN : 0852742223

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Graph Theory by B Andrasfai Pdf

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.

Author : Sergio Camiz
Publisher : World Scientific
Page : 258 pages
File Size : 42,5 Mb
Release : 1996
Category : Economics, Mathematical
ISBN : 9789814530088

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Matrices And Graphs by Sergio Camiz Pdf

Author : Ulrich Knauer
Publisher : Walter de Gruyter
Page : 325 pages
File Size : 44,8 Mb
Release : 2011-09-29
Category : Mathematics
ISBN : 9783110255096

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Algebraic Graph Theory by Ulrich Knauer Pdf

Graph models are extremely useful for almost all applications and applicators as they play an important role as structuring tools. They allow to model net structures – like roads, computers, telephones – instances of abstract data structures – like lists, stacks, trees – and functional or object oriented programming. In turn, graphs are models for mathematical objects, like categories and functors. This highly self-contained book about algebraic graph theory is written with a view to keep the lively and unconventional atmosphere of a spoken text to communicate the enthusiasm the author feels about this subject. The focus is on homomorphisms and endomorphisms, matrices and eigenvalues. It ends with a challenging chapter on the topological question of embeddability of Cayley graphs on surfaces.

Author : Dusanka Janezic,Ante Milicevic,Sonja Nikolic,Nenad Trinajstic
Publisher : CRC Press
Page : 0 pages
File Size : 54,7 Mb
Release : 2015-04-22
Category : Mathematics
ISBN : 1498701159

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Graph-Theoretical Matrices in Chemistry by Dusanka Janezic,Ante Milicevic,Sonja Nikolic,Nenad Trinajstic Pdf

Graph-Theoretical Matrices in Chemistry presents a systematic survey of graph-theoretical matrices and highlights their potential uses. This comprehensive volume is an updated, extended version of a former bestseller featuring a series of mathematical chemistry monographs. In this edition, nearly 200 graph-theoretical matrices are included. This second edition is organized like the previous one—after an introduction, graph-theoretical matrices are presented in five chapters: The Adjacency Matrix and Related Matrices, Incidence Matrices, The Distance Matrix and Related Matrices, Special Matrices, and Graphical Matrices. Each of these chapters is followed by a list of references. Among the matrices presented several are novel and some are known only to a few. The properties and potential usefulness of many of the presented graph-theoretical matrices in chemistry have yet to be investigated. Most of the graph-theoretical matrices presented have been used as sources of molecular descriptors usually referred to as topological indices. They are particularly concerned with a special class of graphs that represents chemical structures involving molecules. Due to its multidisciplinary scope, this book will appeal to a broad audience ranging from chemistry and mathematics to pharmacology.

Author : Ravindra B. Bapat
Publisher : Springer Science & Business Media
Page : 139 pages
File Size : 52,9 Mb
Release : 2008-01-18
Category : Mathematics
ISBN : 9780387226019

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Linear Algebra and Linear Models by Ravindra B. Bapat Pdf

This book provides a rigorous introduction to the basic aspects of the theory of linear estimation and hypothesis testing, covering the necessary prerequisites in matrices, multivariate normal distribution and distributions of quadratic forms along the way. It will appeal to advanced undergraduate and first-year graduate students, research mathematicians and statisticians.

Author : Dragoš M. Cvetković,Peter Rowlinson,Slobodan Simic
Publisher : Cambridge University Press
Page : 284 pages
File Size : 47,5 Mb
Release : 1997-01-09
Category : Mathematics
ISBN : 9780521573528

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Eigenspaces of Graphs by Dragoš M. Cvetković,Peter Rowlinson,Slobodan Simic Pdf

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.