| 图的距离谱综述 |
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| 引用本文： | 林辉球,束金龙,薛杰,张宇珂.图的距离谱综述[J].数学进展,2021(1):29-76. |
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| 作者姓名： | 林辉球 束金龙 薛杰 张宇珂 |
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| 作者单位： | 华东理工大学理学院数学系;华东师范大学计算机科学与技术学院;郑州大学数学与统计学院 |
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| 基金项目： | Supported by NSFC (Nos.11771141,12011530064,12001498)。 |
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| 摘 要： | 设D(G)为连通图G的距离矩阵,λ1(D)≥…≥λn(D)是D(G)的特征值.距离特征值的研究可追溯到Graham和Pollack Bell Syst.Tech.J.,1971,50:2495-2519]的工作,其中描述了负距离特征值数目与数据通信系统寻址问题之间的关系.2014年,Aouchiche和Hansen的综述Linear Algebra Appl.,2014,458:301-386]给出了距离特征值的各种性质.本文中综述了2014-2020年间图的距离特征值研究的新进展.
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| 关 键 词： | 距离矩阵 距离谱 距离谱半径 距离能量 |
A Survey on Distance Spectra of Graphs |
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| LIN Huiqiu,SHU Jinlong,XUE Jie,ZHANG Yuke.A Survey on Distance Spectra of Graphs[J].Advances in Mathematics,2021(1):29-76. |
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| Authors: | LIN Huiqiu SHU Jinlong XUE Jie ZHANG Yuke |
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| Institution: | (Department of Mathematics,School of Science,East China University of Science and Technology,Shanghai,200237,P.R.China;School of Computer Science and Technology,East China Normal University,Shanghai,200062,P.R.China;School of Mathematics and Statistics,Zhengzhou University,Zhengzhou,Henan,450001,P.R.China) |
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| Abstract: | Let D(G) be the distance matrix of a connected graph G and λ1(D)≥…≥λn(D) be the eigenvalues of D(G).The study of distance eigenvalues can be traced back to the work of Graham and Pollack Bell Syst.Tech.J.,1971,50:2495-2519] in which they described a relationship between the number of negative distance eigenvalues and the addressing problem in data communication system.In 2014,Aouchiche and Hansen gave a survey Linear Algebra Appl.,2014,458:301-386] on various properties of distance eigenvalues.In this paper,we report new progress on the distance eigenvalues of graphs from 2014 to 2020. |
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| Keywords: | distance matrix distance spectra distance spectral radius distance energy |
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