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The Mutually Beneficial Relationship of Graphs and Matrices

A co-publication of the AMS and CBMS
Available Formats:
Softcover ISBN: 978-0-8218-5315-3
Product Code: CBMS/115
List Price: $39.00 Individual Price:$31.20
Electronic ISBN: 978-1-4704-1573-0
Product Code: CBMS/115.E
List Price: $36.00 MAA Member Price:$32.40
AMS Member Price: $28.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version. List Price:$58.50
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The Mutually Beneficial Relationship of Graphs and Matrices
A co-publication of the AMS and CBMS
Available Formats:
 Softcover ISBN: 978-0-8218-5315-3 Product Code: CBMS/115
 List Price: $39.00 Individual Price:$31.20
 Electronic ISBN: 978-1-4704-1573-0 Product Code: CBMS/115.E
 List Price: $36.00 MAA Member Price:$32.40 AMS Member Price: $28.80 Bundle Print and Electronic Formats and Save! This product is available for purchase as a bundle. Purchasing as a bundle enables you to save on the electronic version.  List Price:$58.50
• Book Details

CBMS Regional Conference Series in Mathematics
Volume: 1152011; 96 pp
MSC: Primary 05; Secondary 15;

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 Verdière 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.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in graph theory.

• Chapters
• Chapter 1. Some fundamentals
• Chapter 2. Eigenvalues of graphs
• Chapter 3. Rado-Hall theorem and applications
• Chapter 4. Colin de Verdière number
• Chapter 5. Classes of matrices of zeros and ones
• Chapter 6. Matrix sign patterns
• Chapter 7. Eigenvalue inclusion and diagonal products
• Chapter 8. Tournaments
• Chapter 9. Two matrix polytopes
• Chapter 10. Digraphs and eigenvalues of (0,1)-matrices

• Reviews

• This delightful short book ... could be used as a supplemental course book in an upper level undergraduate course or first year graduate course in graph theory. ... its contents are beautiful, current, relevant, accessible to undergraduates, and have the potential to entice the audience to want to learn more.

MAA Reviews
• Request Review Copy
Volume: 1152011; 96 pp
MSC: Primary 05; Secondary 15;

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 Verdière 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.

A co-publication of the AMS and CBMS.

Graduate students and research mathematicians interested in graph theory.

• Chapters
• Chapter 1. Some fundamentals
• Chapter 2. Eigenvalues of graphs
• Chapter 3. Rado-Hall theorem and applications
• Chapter 4. Colin de Verdière number
• Chapter 5. Classes of matrices of zeros and ones
• Chapter 6. Matrix sign patterns
• Chapter 7. Eigenvalue inclusion and diagonal products
• Chapter 8. Tournaments
• Chapter 9. Two matrix polytopes
• Chapter 10. Digraphs and eigenvalues of (0,1)-matrices
• This delightful short book ... could be used as a supplemental course book in an upper level undergraduate course or first year graduate course in graph theory. ... its contents are beautiful, current, relevant, accessible to undergraduates, and have the potential to entice the audience to want to learn more.

MAA Reviews
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