Graphs and Matrices
Graphs and Matrices

Author: Ravindra B. Bapat

Publisher: Springer

Published: 2014-09-19

Total Pages: 197

ISBN-13: 1447165691

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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.

Graphic Algebra
Graphic Algebra

Author: Gary Asp

Publisher:

Published: 1998

Total Pages: 0

ISBN-13: 9781559532792

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With engaging activities that students complete with graphing calculators or software, "Graphic Algebra" helps students develop new insights into algebra by providing easy-to-use lessons. (Education/Teaching)

Topics in Algebraic Graph Theory
Topics in Algebraic Graph Theory

Author: Lowell W. Beineke

Publisher: Cambridge University Press

Published: 2004-10-04

Total Pages: 302

ISBN-13: 9780521801973

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There is no other book with such a wide scope of both areas of algebraic graph theory.

Graph Algorithms in the Language of Linear Algebra
Graph Algorithms in the Language of Linear Algebra

Author: Jeremy Kepner

Publisher: SIAM

Published: 2011-01-01

Total Pages: 388

ISBN-13: 9780898719918

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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.

Functions and Graphs
Functions and Graphs

Author: I. M. Gelfand

Publisher: Courier Corporation

Published: 2002-01-01

Total Pages: 116

ISBN-13: 0486425649

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This volume presents students with problems and exercises designed to illuminate the properties of functions and graphs. The 1st part of the book employs simple functions to analyze the fundamental methods of constructing graphs. The 2nd half deals with more complicated and refined questions concerning linear functions, quadratic trinomials, linear fractional functions, power functions, and rational functions. 1969 edition.