双星图的LI矩阵的Ky Fan k-范数  

Ky Fan k -norm of LI matrices for double-star graphs

作　　者：郑馨 戴浩波 金启宇 ZHENG Xin;DAI Haobo;JIN Qiyu(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232000,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232000

出　　处：《哈尔滨商业大学学报（自然科学版）》2024年第3期342-345,共4页Journal of Harbin University of Commerce：Natural Sciences Edition

摘　　要：树是连通的无圈图,研究树的拉普拉斯矩阵具有重要的图论和实际意义.设G是一个有n个点和m个边的图,A(G)和D(G)分别是图G的邻接矩阵和对角度矩阵,那么G的拉普拉斯矩阵定义为L(G)=D(G)-A(G).LI矩阵定义为LI(G)=L(G)-(2m/n)I_(n),其中I_(n)是单位矩阵.图的LI矩阵的Ky Fan k-范数代表了拉普拉斯特征值和拉普拉斯特征值平均值之间距离的有序和.研究了双星图的LI矩阵的Ky Fan k-范数,证明了双星图的LI矩阵的Ky Fan k-范数满足文献[6]中提出的猜想.Trees are connected acyclic graphs.The study of the Laplacian matrix of trees has important graph-theoretic and practical significance.It has a wide range of important applications in computer networks,biology and chemistry.Let G be a graph with n vertices and m edges.Let A(G)and D(G)be the adjacency matrix and the degree diagonal matrix of a graph G,respectively.Then L(G)=D(G)-A(G)is called Laplacian matrix of the graph G.The LI-matrix of G are defined as LI(G)=L(G)-(2m/n)I_(n),where I_(n) is the identity matrix.The Ky Fan k-norm of the LI-matrix of graphs represents the ordered sum of the distance between Laplacian eigenvalues and the average of all Laplacian eigenvalues.This paper was interested in the Ky Fan k-norm of the LI-matrix of double-star graphs and proved that the Ky Fan k-norm of LI matrices of double-star graphs satisfy the conjecture presented in the literature[6].

关 键 词：双星图 拉普拉斯矩阵 LI矩阵 Ky Fan k-范数 能量 奇异值 

分 类 号：O157.6[理学—数学]