Author : Miroslav Fiedler
Publisher : Cambridge University Press
Page : 206 pages
File Size : 50,3 MB
Release : 2011-02-03
Category : Mathematics
ISBN : 0521461936
Demonstrates the close relationship between matrix theory and elementary Euclidean geometry, with emphasis on using simple graph-theoretical notions.
Author : Ravindra B. Bapat
Publisher : Springer
Page : 197 pages
File Size : 18,60 MB
Release : 2014-09-19
Category : Mathematics
ISBN : 1447165691
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 : D. Logofet
Publisher : CRC Press
Page : 383 pages
File Size : 48,26 MB
Release : 2018-02-01
Category : Science
ISBN : 1351091220
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
Publisher : Springer Science & Business Media
Page : 254 pages
File Size : 23,14 MB
Release : 2012-12-06
Category : Mathematics
ISBN : 1461383692
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 : Alan Frieze
Publisher : Cambridge University Press
Page : 483 pages
File Size : 18,28 MB
Release : 2016
Category : Mathematics
ISBN : 1107118506
The text covers random graphs from the basic to the advanced, including numerous exercises and recommendations for further reading.
Author : John Harris
Publisher : Springer Science & Business Media
Page : 392 pages
File Size : 43,31 MB
Release : 2009-04-03
Category : Mathematics
ISBN : 0387797114
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.
Author : Zhexian Wan
Publisher : World Scientific
Page : 396 pages
File Size : 21,47 MB
Release : 1996
Category : Mathematics
ISBN : 9789810226381
The present monograph is a state-of-art survey of the geometry of matrices whose study was initiated by L K Hua in the forties. The geometry of rectangular matrices, of alternate matrices, of symmetric matrices, and of hermitian matrices over a division ring or a field are studied in detail. The author's recent results on geometry of symmetric matrices and of hermitian matrices are included. A chapter on linear algebra over a division ring and one on affine and projective geometry over a division ring are also included. The book is clearly written so that graduate students and third or fourth year undergraduate students in mathematics can read it without difficulty.
Author : Fan R. K. Chung
Publisher : American Mathematical Soc.
Page : 228 pages
File Size : 32,63 MB
Release : 1997
Category : Mathematics
ISBN : 0821803158
This text discusses spectral graph theory.
Author : Richard J. Trudeau
Publisher : Courier Corporation
Page : 242 pages
File Size : 10,94 MB
Release : 2013-04-15
Category : Mathematics
ISBN : 0486318664
Aimed at "the mathematically traumatized," this text offers nontechnical coverage of graph theory, with exercises. Discusses planar graphs, Euler's formula, Platonic graphs, coloring, the genus of a graph, Euler walks, Hamilton walks, more. 1976 edition.
Author : Karim Adiprasito
Publisher : Springer
Page : 277 pages
File Size : 37,49 MB
Release : 2016-05-02
Category : Mathematics
ISBN : 3319281860
This volume presents easy-to-understand yet surprising properties obtained using topological, geometric and graph theoretic tools in the areas covered by the Geometry Conference that took place in Mulhouse, France from September 7–11, 2014 in honour of Tudor Zamfirescu on the occasion of his 70th anniversary. The contributions address subjects in convexity and discrete geometry, in distance geometry or with geometrical flavor in combinatorics, graph theory or non-linear analysis. Written by top experts, these papers highlight the close connections between these fields, as well as ties to other domains of geometry and their reciprocal influence. They offer an overview on recent developments in geometry and its border with discrete mathematics, and provide answers to several open questions. The volume addresses a large audience in mathematics, including researchers and graduate students interested in geometry and geometrical problems.
