图的距离谱综述  

A Survey on Distance Spectra of Graphs

作　　者：林辉球 束金龙[2] 薛杰 张宇珂 LIN Huiqiu;SHU Jinlong;XUE Jie;ZHANG Yuke(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)

机构地区：[1]华东理工大学理学院数学系,上海200237 [2]华东师范大学计算机科学与技术学院,上海200062 [3]郑州大学数学与统计学院,河南郑州450001

出　　处：《数学进展》2021年第1期29-76,共48页Advances in Mathematics（China）

基　　金：Supported by NSFC (Nos.11771141,12011530064,12001498)。

摘　　要：设D(G)为连通图G的距离矩阵,λ_(1)(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.Let D(G) be the distance matrix of a connected graph G and λ_(1)(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.

关 键 词：距离矩阵 距离谱 距离谱半径 距离能量 

分 类 号：O157.5[理学—数学]