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内容简介

　　《图的谱半径（英文版）》主要介绍了图的相邻矩阵谱半径的相关知识，包括频谱分解、佩龙-弗罗宾尼斯定理、瑞利商等，同时也包括一些作者从未发表过的研究成果，可使读者很好地掌握图的谱半径相关知识。《图的谱半径（英文版）》内容全面，知识点丰富，适合高等院校师生和数学爱好者参考阅读。

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 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

精彩书摘

　　《图的谱半径（英文版）》：
　　Graph theorists are relying on computers nowadays to pretest their ideasand conjectures， whether they write their own programs or use ready—made software， such as Graffiti （58）， GRAPH （48）， newGRAPH （144），AutoGraphiX （27）， Grlnvln （121）， or MathChem （158）.Notable softwareamong these is AutoGraphiX， which employs the Variable Neighborhood Search metaheuristic in the search for graphs that attain extremal value ofuser—defined functions in various graph classes.The use of AutoGraphiXhas been infiuential in devising a number ofresults presented in this chapter，especially in the case of determining extremal values of the spectral radiusamong connected graphs with a constant value of a selected integer—valuedinvariant.Some hard conjectures obtained with the help of AutoGraphiXare reviewed in Section 4.1， while results on the graphs with the minimumor the maximum spectral radius among graphs with a given value of theclique number， chromatic number， independence number， matching number，diameter， radius， and domination number are presented in Sections 4.2—4.8.Finally， nearly complete solution to one of the hard conjectures fromSection 4.1 is presented in Section 4.9.
　　……

前言/序言

图的谱半径（英文版） [Spectral Radius Of Graphs] 电子书 下载 mobi epub pdf txt

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