Softcover ISBN:  9780821853153 
Product Code:  CBMS/115 
List Price:  $39.00 
Individual Price:  $31.20 
Electronic ISBN:  9781470415730 
Product Code:  CBMS/115.E 
List Price:  $36.00 
MAA Member Price:  $32.40 
AMS Member Price:  $28.80 

Book DetailsCBMS Regional Conference Series in MathematicsVolume: 115; 2011; 96 ppMSC: 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 RadoHall 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 wellknown 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 copublication of the AMS and CBMS.
ReadershipGraduate students and research mathematicians interested in graph theory.

Table of Contents

Chapters

Chapter 1. Some fundamentals

Chapter 2. Eigenvalues of graphs

Chapter 3. RadoHall 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


Additional Material

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


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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 RadoHall 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 wellknown 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 copublication 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. RadoHall 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