Graph Algebra

Author : Courtney Brown
Publisher : SAGE
ISBN 13 : 1412941091
Total Pages : 105 pages
Book Rating : 4.99/5 ( download)

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Download or read book Graph Algebra written by Courtney Brown and published by SAGE. This book was released on 2008 with total page 105 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 1447165691
Total Pages : 197 pages
Book Rating : 4.99/5 ( download)

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Download or read book Graphs and Matrices written by Ravindra B. Bapat and published by Springer. This book was released on 2014-09-19 with total page 197 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Iain Raeburn
Publisher : American Mathematical Soc.
ISBN 13 : 0821836609
Total Pages : 130 pages
Book Rating : 4.06/5 ( download)

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Download or read book Graph Algebras written by Iain Raeburn and published by American Mathematical Soc.. This book was released on 2005 with total page 130 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Chris Godsil
Publisher : Springer Science & Business Media
ISBN 13 : 1461301637
Total Pages : 453 pages
Book Rating : 4.39/5 ( download)

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Download or read book Algebraic Graph Theory written by Chris Godsil and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 453 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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 : Jeremy Kepner
Publisher : SIAM
ISBN 13 : 9780898719918
Total Pages : 388 pages
Book Rating : 4.17/5 ( download)

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Download or read book Graph Algorithms in the Language of Linear Algebra written by Jeremy Kepner and published by SIAM. This book was released on 2011-01-01 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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
ISBN 13 : 9780521801973
Total Pages : 302 pages
Book Rating : 4.74/5 ( download)

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Download or read book Topics in Algebraic Graph Theory written by Lowell W. Beineke and published by Cambridge University Press. This book was released on 2004-10-04 with total page 302 pages. Available in PDF, EPUB and Kindle. Book excerpt: There is no other book with such a wide scope of both areas of algebraic graph theory.

Author : Lynn Marecek
Publisher :
ISBN 13 : 9781951693848
Total Pages : pages
Book Rating : 4.41/5 ( download)

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Download or read book Intermediate Algebra 2e written by Lynn Marecek and published by . This book was released on 2020-05-06 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Norman Biggs
Publisher : Cambridge University Press
ISBN 13 : 9780521458979
Total Pages : 220 pages
Book Rating : 4.78/5 ( download)

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Download or read book Algebraic Graph Theory written by Norman Biggs and published by Cambridge University Press. This book was released on 1993 with total page 220 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Hartmut Ehrig
Publisher : Springer Science & Business Media
ISBN 13 : 3540311882
Total Pages : 383 pages
Book Rating : 4.81/5 ( download)

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Download or read book Fundamentals of Algebraic Graph Transformation written by Hartmut Ehrig and published by Springer Science & Business Media. This book was released on 2006-05-01 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is the first textbook treatment of the algebraic approach to graph transformation, based on algebraic structures and category theory. It contains an introduction to classical graphs. Basic and advanced results are first shown for an abstract form of replacement systems and are then instantiated to several forms of graph and Petri net transformation systems. The book develops typed attributed graph transformation and contains a practical case study.

Author : Ulrich Knauer
Publisher : Walter de Gruyter
ISBN 13 : 311025509X
Total Pages : 325 pages
Book Rating : 4.96/5 ( download)

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Download or read book Algebraic Graph Theory written by Ulrich Knauer and published by Walter de Gruyter. This book was released on 2011-09-29 with total page 325 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.