Author : Courtney Brown
Publisher : SAGE
Page : 105 pages
File Size : 48,50 MB
Release : 2008
Category : Mathematics
ISBN : 1412941091
This 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
Page : 197 pages
File Size : 40,30 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 : Jeremy Kepner
Publisher : SIAM
Page : 388 pages
File Size : 43,67 MB
Release : 2011-01-01
Category : Mathematics
ISBN : 9780898719918
The 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 : Lowell W. Beineke
Publisher : Cambridge University Press
Page : 302 pages
File Size : 45,47 MB
Release : 2004-10-04
Category : Mathematics
ISBN : 9780521801973
There is no other book with such a wide scope of both areas of algebraic graph theory.
Author : Iain Raeburn
Publisher : American Mathematical Soc.
Page : 130 pages
File Size : 18,63 MB
Release : 2005
Category : Mathematics
ISBN : 0821836609
Graph 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 : Ilwoo Cho
Publisher : CRC Press
Page : 446 pages
File Size : 37,64 MB
Release : 2013-09-11
Category : Mathematics
ISBN : 146659019X
This 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 : Lynn Marecek
Publisher :
Page : pages
File Size : 43,47 MB
Release : 2020-05-06
Category :
ISBN : 9781951693848
Author : Andrei Kelarev
Publisher : CRC Press
Page : 388 pages
File Size : 12,91 MB
Release : 2003-07-08
Category : Mathematics
ISBN : 9780824747084
Graph algebras possess the capacity to relate fundamental concepts of computer science, combinatorics, graph theory, operations research, and universal algebra. They are used to identify nontrivial connections across notions, expose conceptual properties, and mediate the application of methods from one area toward questions of the other four. After a concentrated review of the prerequisite mathematical background, Graph Algebras and Automata defines graph algebras and reveals their applicability to automata theory. It proceeds to explore assorted monoids, semigroups, rings, codes, and other algebraic structures and to outline theorems and algorithms for finite state automata and grammars.
Author : Chris Godsil
Publisher : Springer Science & Business Media
Page : 453 pages
File Size : 22,70 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461301637
This 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 : Norman Biggs
Publisher : Cambridge University Press
Page : 220 pages
File Size : 25,70 MB
Release : 1993
Category : Mathematics
ISBN : 9780521458979
This is a substantial revision of a much-quoted monograph, first published in 1974. The structure is unchanged, but the text has been clarified and the notation brought into line with current practice. A large number of 'Additional Results' are included at the end of each chapter, thereby covering most of the major advances in the last twenty years. Professor Biggs' basic aim remains to express properties of graphs in algebraic terms, then to deduce theorems about them. In the first part, he tackles the applications of linear algebra and matrix theory to the study of graphs; algebraic constructions such as adjacency matrix and the incidence matrix and their applications are discussed in depth. There follows an extensive account of the theory of chromatic polynomials, a subject which has strong links with the 'interaction models' studied in theoretical physics, and the theory of knots. The last part deals with symmetry and regularity properties. Here there are important connections with other branches of algebraic combinatorics and group theory. This new and enlarged edition this will be essential reading for a wide range of mathematicians, computer scientists and theoretical physicists.
