Author: Dragoš M. Cvetković,Peter Rowlinson,Slobodan Simic

Publisher: Cambridge University Press

ISBN: 9780521573528

Category: Mathematics

Page: 258

View: 5267

This book describes the spectral theory of finite graphs.

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# Search Results for: **eigenspaces-of-graphs-encyclopedia-of-mathematics-and-its-applications**

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This book describes the spectral theory of finite graphs.

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Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.

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The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

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

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This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

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Vols. 41-44, 46-50 include Sonderheft: Vorträge der wissenschaftlichen Jahrestagung der Gesellschaft für Angewandte Mathematik und Mechanik (v. 44, Vorträge der Tagung für Angewandte Mathematik und Mechanik).

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Author: Dragoš M. Cvetković,Peter Rowlinson,Slobodan Simic

Publisher: Cambridge University Press

ISBN: 9780521573528

Category: Mathematics

Page: 258

View: 5267

This book describes the spectral theory of finite graphs.

Author: Richard A. Brualdi

Publisher: American Mathematical Soc.

ISBN: 0821853155

Category: Mathematics

Page: 96

View: 8275

Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. In one direction, knowledge about one of the graphs that can be associated with a matrix can be used to illuminate matrix properties and to get better information about the matrix. Examples include the use of digraphs to obtain strong results on diagonal dominance and eigenvalue inclusion regions and the use of the Rado-Hall theorem to deduce properties of special classes of matrices. Going the other way, linear algebraic properties of one of the matrices associated with a graph can be used to obtain useful combinatorial information about the graph. The adjacency matrix and the Laplacian matrix are two well-known matrices associated to a graph, and their eigenvalues encode important information about the graph. Another important linear algebraic invariant associated with a graph is the Colin de Verdiere number, which, for instance, characterizes certain topological properties of the graph. This book is not a comprehensive study of graphs and matrices. The particular content of the lectures was chosen for its accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more.

Author: Charles R. Johnson,Carlos M. Saiago

Publisher: Cambridge University Press

ISBN: 1108547036

Category: Mathematics

Page: N.A

View: 681

The arrangement of nonzero entries of a matrix, described by the graph of the matrix, limits the possible geometric multiplicities of the eigenvalues, which are far more limited by this information than algebraic multiplicities or the numerical values of the eigenvalues. This book gives a unified development of how the graph of a symmetric matrix influences the possible multiplicities of its eigenvalues. While the theory is richest in cases where the graph is a tree, work on eigenvalues, multiplicities and graphs has provided the opportunity to identify which ideas have analogs for non-trees, and those for which trees are essential. It gathers and organizes the fundamental ideas to allow students and researchers to easily access and investigate the many interesting questions in the subject.

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 3756

*Invited Papers for the ... British Combinatorial Conference*

Author: Anthony Hilton,John Talbot

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 3774

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Combinatorial analysis

Page: N.A

View: 3660

Author: H. M. Mulder,A. Vijayakumar

Publisher: Allied Publishers (India)

ISBN: 9788170239017

Category: Graph theory

Page: 125

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Author: N.A

Publisher: N.A

ISBN: N.A

Category: Engineering design

Page: N.A

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Author: N.A

Publisher: N.A

ISBN: N.A

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Page: N.A

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Author: Lowell W. Beineke,Robin J. Wilson

Publisher: Cambridge University Press

ISBN: 9780521801973

Category: Mathematics

Page: 276

View: 4446

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

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Mathematics

Page: N.A

View: 737

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Chemistry

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View: 1167

Author: Arthur James Wells

Publisher: N.A

ISBN: N.A

Category: English literature

Page: N.A

View: 1719

Author: R. B. Bapat,T. E. S. Raghavan

Publisher: Cambridge University Press

ISBN: 9780521571678

Category: Mathematics

Page: 336

View: 2500

This book provides an integrated treatment of the theory of nonnegative matrices (matrices with only positive numbers or zero as entries) and some related classes of positive matrices, concentrating on connections with game theory, combinatorics, inequalities, optimisation and mathematical economics. The wide variety of applications, which include price fixing, scheduling and the fair division problem, have been carefully chosen both for their elegant mathematical content and for their accessibility to students with minimal preparation. Many results in matrix theory are also presented. The treatment is rigorous and almost all results are proved completely. These results and applications will be of great interest to researchers in linear programming, statistics and operations research. The minimal prerequisites also make the book accessible to first-year graduate students.

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Publisher: N.A

ISBN: N.A

Category: American literature

Page: N.A

View: 7463

*Classification to Eye estimate*

Author: Samuel Kotz,Norman Lloyd Johnson

Publisher: Wiley-Interscience

ISBN: N.A

Category: Mathematics

Page: 624

View: 5372

Author: Samuel Kotz,Norman Lloyd Johnson,Campbell B. Read

Publisher: N.A

ISBN: N.A

Category: Mathematical statistics

Page: N.A

View: 4968

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Engineering

Page: N.A

View: 6913

Vols. 41-44, 46-50 include Sonderheft: Vorträge der wissenschaftlichen Jahrestagung der Gesellschaft für Angewandte Mathematik und Mechanik (v. 44, Vorträge der Tagung für Angewandte Mathematik und Mechanik).

Author: N.A

Publisher: N.A

ISBN: N.A

Category: Bibliography, National

Page: N.A

View: 5673

*Vorlesungen*

Author: Philipp Rothmaler

Publisher: Spektrum Akademischer Verlag

ISBN: 9783860254615

Category: Model theory

Page: 331

View: 6494