【目 录】
Preface iii
Chapter 1 Introduction //1
1.1 Graphs and Their lnvariants //1
1.2 Adjacency Matrix, Its Eigenvalues, and Its Characteristic Polynomial //4
1.3 Some Useful Tools from Matrix Theory //8
Chapter 2 Properties of the Principal Eigenvector //15
2.1 Proportionality Lemma and the Rooted Product //15
2.2 Principal Eigenvector Components Along a Path //21
2.3 Extremal Components of the Principal Eigenvector //28
2.4 Optimally Decreasing Spectral Radius by Deleting Vertices or Edges //35
2.5 Regular, Harmonic, and Semiharmonic Graphs //47
Chapter 3 Spectral Radius of Particular Types of Graphs //53
3.1 Nonregular Graphs //53
3.2 Graphs with a Given Degree Sequence //62
3.3 Graphs with a Few Edges //68
3.4 Complete Multipartite Graphs //77
Chapter 4 Spectral Radius and Other Graph Invariants //87
4.1 Selected AutoGraphiX Conjectures //87
4.2 Clique Number //89
4.3 Chromatic Number //93
4.4 IndependenceNumber //95
4.5 Matching Number //98
4.6 The Diameter //101
4.7 The Radius //117
4.8 The Domination Number //125
4.9 Nordhaus-Gaddum Inequality for the Spectral Radius //140
Bibliography //147
Index //155