Contents Preface ix Chapter 1. Some Fundamentals 1 1.1. Nonnegative Matrices 1 1.2. Symmetric Matrices 7 Bibliography 11 Chapter 2. Eigenvalues of Graphs 13 2.1. Some Basic Properties 13 2.2. Eigenvalues and Graph Parameters 16 2.3. Graphs with small λmax 19 2.4. Laplacian Matrix of a Graph 21 Bibliography 23 Chapter 3. Rado-Hall Theorem and Applications 25 3.1. Rado-Hall Theorem 25 3.2. Applications 27 Bibliography 31 Chapter 4. Colin de Verdi` ere Number 33 4.1. Motivation and Definition 33 4.2. Colin de Verdi` ere Number and Graph Properties 35 Bibliography 38 Chapter 5. Classes of Matrices of Zeros and Ones 39 5.1. Equivalent Formulations 39 5.2. The Classes A(R, S) 40 5.3. A Generalization 45 Bibliography 47 Chapter 6. Matrix Sign Patterns 49 6.1. Sign-Nonsingular Matrices 49 6.2. An Application 53 6.3. Spectrally Arbitrary Sign Patterns 55 Bibliography 57 Chapter 7. Eigenvalue Inclusion and Diagonal Products 59 7.1. Some Classical Theorems 59 7.2. Diagonal Products and Nonsingularity 62 vii
Previous Page Next Page