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Author: Courtney Brown
Publisher: SAGE
Published: 2008
Total Pages: 105
ISBN-13: 1412941091
DOWNLOAD EBOOKThis book describes an easily applied language of mathematical modeling that uses boxes and arrows to develop very sophisticated, algebraic statements of social and political phenomena.
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: Iain Raeburn
Publisher: American Mathematical Soc.
Published: 2005
Total Pages: 130
ISBN-13: 0821836609
DOWNLOAD EBOOKGraph algebras are a family of operator algebras which are associated to directed graphs. These algebras have an attractive structure theory in which algebraic properties of the algebra are related to the behavior of paths in the underlying graph. In the past few years there has been a great deal of activity in this area, and graph algebras have cropped up in a surprising variety of situations, including non-abelian duality, non-commutative geometry, and the classification of simple $C*$-algebras. The first part of the book provides an introduction to the subject suitable for students who have seen a first course on the basics of $C*$-algebras. In the second part, the author surveys the literature on the structure theory of graph algebras, highlights some applications of this theory, and discusses several recent generalizations which seem particularly promising. The volume is suitable for graduate students and research mathematicians interested in graph theory and operator algebras.
Author: Jeremy Kepner
Publisher: SIAM
Published: 2011-01-01
Total Pages: 388
ISBN-13: 9780898719918
DOWNLOAD EBOOKThe 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.
Author: Ilwoo Cho
Publisher: CRC Press
Published: 2013-09-11
Total Pages: 446
ISBN-13: 146659019X
DOWNLOAD EBOOKThis book introduces the study of algebra induced by combinatorial objects called directed graphs. These graphs are used as tools in the analysis of graph-theoretic problems and in the characterization and solution of analytic problems. The book presents recent research in operator algebra theory connected with discrete and combinatorial mathematical objects. It also covers tools and methods from a variety of mathematical areas, including algebra, operator theory, and combinatorics, and offers numerous applications of fractal theory, entropy theory, K-theory, and index theory.
Author: Chris Godsil
Publisher: Springer Science & Business Media
Published: 2013-12-01
Total Pages: 453
ISBN-13: 1461301637
DOWNLOAD EBOOKThis book presents and illustrates the main tools and ideas of algebraic graph theory, with a primary emphasis on current rather than classical topics. It is designed to offer self-contained treatment of the topic, with strong emphasis on concrete examples.
Author: Lynn Marecek
Publisher:
Published: 2020-05-06
Total Pages:
ISBN-13: 9781951693848
DOWNLOAD EBOOKAuthor: Lowell W. Beineke
Publisher: Cambridge University Press
Published: 2004-10-04
Total Pages: 302
ISBN-13: 1107079454
DOWNLOAD EBOOKThe 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.
Author: Zoran Stanić
Publisher: Cambridge University Press
Published: 2015-07-23
Total Pages: 311
ISBN-13: 1107545978
DOWNLOAD EBOOKThis book explores the inequalities for eigenvalues of the six matrices associated with graphs. Includes the main results and selected applications.
Author: Mark Illingworth
Publisher:
Published: 1995
Total Pages: 0
ISBN-13: 9781559530774
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