TY  - BOOK
AU  - Brualdi, Richard A.
AU  - Brualdi, Richard A.
TI  - The Mutually Beneficial Relationship of Graphs and Matrices
T2  - Regional conference series in mathematics, no. 115
SN  - 9781470437220
U1  - 511.55  BRU 
PY  - 2017///
CY  - New Delhi
PB  - :University Press
KW  - Mathematics
KW  - General principles of mathematics
KW  - Matrices
KW  - Graph theory
KW  - Algebras, Linear
KW  - Combinatorial analysis
KW  - Matrix
KW  - Number Theory
N1  - Machine generated contents note: 1.1.Nonnegative Matrices --
1.2.Symmetric Matrices --
Bibliography --
2.1.Some Basic Properties --
2.2.Eigenvalues and Graph Parameters --
2.3.Graphs with small Amax --
2.4.Laplacian Matrix of a Graph --
Bibliography --
3.1.Rado-Hall Theorem --
3.2.Applications --
Bibliography --
4.1.Motivation and Definition --
4.2.Colin de Verdiere Number and Graph Properties --
Bibliography --
5.1.Equivalent Formulations --
5.2.The Classes A(R, S) --
5.3.A Generalization --
Bibliography --
6.1.Sign-Nonsingular Matrices --
6.2.An Application --
6.3.Spectrally Arbitrary Sign Patterns --
Bibliography --
7.1.Some Classical Theorems --
7.2.Diagonal Products and Nonsingularity --
Bibliography --
8.1.Landau's Theorem --
8.2.A Special Tournament in T(R) --
8.3.Eigenvalues of Tournament Matrices --
Bibliography --
9.1.The Doubly Stochastic Polytope --
9.2.Alternating Sign Matrices --
9.3.The Alternating Sign Matrix Polytope --
9.4.ASM Patterns --
Bibliography Note continued: 10.1.(0, 1)-matrices with all Eigenvalues Positive --
10.2.Totally Nonnegative Matrices --
10.3.Totally Nonnegative (0, 1)-matrices --
Bibliography
N2  - Graphs and matrices enjoy a fascinating and mutually beneficial relationship. This interplay has benefited both graph theory and linear algebra. This is not a comprehensive study of graphs and matrices, instead the contributions have been chosen for their accessibility, beauty, and current relevance, and for the possibility of enticing the audience to want to learn more
ER  -