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Author: Miroslav Fiedler
Publisher: Cambridge University Press
Published: 2011-02-03
Total Pages: 206
ISBN-13: 0521461936
DOWNLOAD EBOOKDemonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.
Author: Miroslav Fiedler
Publisher:
Published: 2011
Total Pages: 197
ISBN-13: 9780511973611
DOWNLOAD EBOOK"This book comprises, in addition to auxiliary material, the research on which I have worked for the past more than 50 years. Some of the results appear here for the first time. The impetus for writing the book came from the late Victor Klee, after my talk in Minneapolis in 1991. The main subject is simplex geometry, a topic which fascinated me from my student times, caused, in fact, by the richness of triangle and tetrahedron geometry on one side and matrix theory on the other side. A large part of the content is concerned with qualitative properties of a simplex. This can be understood as studying not just relations of equalities but also inequalities. It seems that this direction is starting to have important consequences in practical (and important) applications, such as finite element methods"--Provided by publisher.
Author: Ravindra B. Bapat
Publisher: Springer
Published: 2014-09-19
Total Pages: 197
ISBN-13: 1447165691
DOWNLOAD EBOOKThis 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: J. J. Seidel
Publisher: Academic Press
Published: 2014-05-10
Total Pages: 431
ISBN-13: 1483268004
DOWNLOAD EBOOKGeometry and Combinatorics: Selected Works of J. J. Seidel brings together some of the works of J. J. Seidel in geometry and combinatorics. Seidel's selected papers are divided into four areas: graphs and designs; lines with few angles; matrices and forms; and non-Euclidean geometry. A list of all of Seidel's publications is included. Comprised of 29 chapters, this book begins with a discussion on equilateral point sets in elliptic geometry, followed by an analysis of strongly regular graphs of L2-type and of triangular type. The reader is then introduced to strongly regular graphs with (-1, 1, 0) adjacency matrix having eigenvalue 3; graphs related to exceptional root systems; and equiangular lines. Subsequent chapters deal with the regular two-graph on 276 vertices; the congruence order of the elliptic plane; equi-isoclinic subspaces of Euclidean spaces; and Wielandt's visibility theorem. This monograph will be of interest to students and practitioners in the field of mathematics.
Author: D. Logofet
Publisher: CRC Press
Published: 2018-02-01
Total Pages: 383
ISBN-13: 1351091220
DOWNLOAD EBOOKIntuitive 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: Jason J. Molitierno
Publisher: CRC Press
Published: 2016-04-19
Total Pages: 425
ISBN-13: 1439863393
DOWNLOAD EBOOKOn 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: László Lovász
Publisher:
Published: 2019
Total Pages: 444
ISBN-13: 9781470453541
DOWNLOAD EBOOKGraphs are usually represented as geometric objects drawn in the plane, consisting of nodes and curves connecting them. The main message of this book is that such a representation is not merely a way to visualize the graph, but an important mathematical tool. It is obvious that this geometry is crucial in engineering, for example, if you want to understand rigidity of frameworks and mobility of mechanisms. But even if there is no geometry directly connected to the graph-theoretic problem, a well-chosen geometric embedding has mathematical meaning and applications in proofs and algorithms. This.
Author: Donald Cohen
Publisher: Donald Cohen
Published: 1995
Total Pages: 88
ISBN-13: 0962167436
DOWNLOAD EBOOKAuthor: Rees
Publisher: Routledge
Published: 2017-07-12
Total Pages: 350
ISBN-13: 1351444379
DOWNLOAD EBOOKExamines 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
Published: 2010-07-23
Total Pages: 175
ISBN-13: 1848829817
DOWNLOAD EBOOKGraphs 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.
