图的一种加权邻接矩阵谱半径和能量的界  

Bounds for the spectral radius and energy of a kind of weighted adjacency matrix of graphs

作　　者：卢鹏丽[1] 薛小燕 LU Peng-li;XUE Xiao-yan(School of Computer and Communication,Lanzhou Univ.of Tech.,Lanzhou 730050,China)

机构地区：[1]兰州理工大学计算机与通信学院,甘肃兰州730050

出　　处：《兰州理工大学学报》2023年第1期144-151,共8页Journal of Lanzhou University of Technology

基　　金：国家自然科学基金(11361033,11861045,62162040)。

摘　　要：图G的一种加权邻接矩阵记为A_(db)(G)=(a^(db)_(ij))_(n×n),若顶点v_(i)和顶点v_(j)相邻,则a^(db)_(ij)=d_(i)+d_(j)/d_(i)d_(j),反之a^(db)_(ij)=0.给出图G的加权谱半径的上下界,并在此基础上给出加权谱半径的Nordhaus-Gaddum-type关系.得到了图G的加权能量的几个上下界,并在此基础上给出加权能量的Nordhaus-Gaddum-type关系.A kind of weighted adjacency matrix of graph G is denoted by A_(db)(G)=(a^(db)_(ij))_(n×n),where a^(db)_(ij)=d_(i)+d_(j)/d_(i)d_(j)if the vertices v_(i)and v_(j)are adjacent,and a^(db)_(ij)=0 otherwise.In this paper,some upper and lower bounds of the weighted spectral radius of graph G are first obtained,and then the Nordhaus-Gaddum-type relation for weighted spectral radius is given.In addition,several upper and lower bounds for the weighted energy are obtained,then,the Nordhaus-Gaddum-type results for the weighted energy are presented.

关 键 词：一种加权邻接矩阵 加权谱半径 加权能量 Nordhaus-Gaddum-type关系 

分 类 号：O157.5[理学—数学] O157.6[理学—基础数学]