《圖的譜半徑(英文版)》主要介紹了圖的相鄰矩陣譜半徑的相關(guān)知識(shí),包括頻譜分解、佩龍-弗羅賓尼斯定理、瑞利商等,同時(shí)也包括一些作者從未發(fā)表過的研究成果,可使讀者很好地掌握?qǐng)D的譜半徑相關(guān)知識(shí)!秷D的譜半徑(英文版)》內(nèi)容全面,知識(shí)點(diǎn)豐富,適合高等院校師生和數(shù)學(xué)愛好者參考閱讀。
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 of the 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 Spectral Radius and Other Graph Invariants
4.1 Selected AutoGraphiX Conjectures
4.2 Clique Number
4.3 Chromatic Number
4.4 Independence Number
4.5 Matching Number
4.6 The Diameter
4.7 The Radius
4.8 The Domination Number
4.9 Nordhaus-Gaddum Inequality for the Spectral Radius
Bibliography
Index