内容介绍
本书首先对图、邻接矩阵及其特征值、特征多项式等基础知识进行了介绍,其次介绍了主特征向量的相关性质,特殊类型图的谱半径等内容。书中还涉及谱分解、Perron-Frobenius定理、瑞利商、Weyl定理以及交错定理等内容。
图的谱半径
目录
●Preface
●Chapter 1 Introduction
●1.1 Graphs and Their Invariants
●1.2 Adjacency Matrix,Its Eigenvalues,and Its Characteristic Polynomial
●1.3 Some Useful Tools from Matrix Theory
●Chapter 2 Properties ofthe Principal Eigenvector
●2.1 Proportionality Lemma and the Rooted Product
●2.2 Principal Eigenvector Components Along a Path
●2.3 Extremal Components of the Principal Eigenvector
●2.4 Optimally Decreasing Spectral Radius by Deleting Vertices or Edges
●2.5 Regular, Harmonic, and Semiharmonic Graphs
●Chapter 3 Spectral Radius of Particular Types of Graphs
●3.1 Nonregular Graphs
●3.2 Graphs with a Given Degree Sequence
●3.3 Graphs with a Few Edges
●3.4 Complete Multipartite Graphs
●Chapter 4 SDectral Radius and Other Graph Invariants
●4.1 Selected AutoGraphiX Conjectures
●4.2 Clique Numbei
●4.3 Chromatic Number......
内容介绍
本书首先对图、邻接矩阵及其特征值、特征多项式等基础知识进行了介绍,其次介绍了主特征向量的相关性质,特殊类型图的谱半径等内容。书中还涉及谱分解、Perron-Frobenius定理、瑞利商、Weyl定理以及交错定理等内容。
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