高校应用数学学报2024，Vol.39Issue(4) ：493-500.

关于树补图的Aα-谱半径的一些极值结论

Some extremal results on the Aα-spectral radius of the complement graphs of trees

彭家荣 朱艳丽 张蓝
高校应用数学学报2024，Vol.39Issue(4) ：493-500.
✕
  • 万方数据

关于树补图的Aα-谱半径的一些极值结论

Some extremal results on the Aα-spectral radius of the complement graphs of trees

彭家荣 1朱艳丽 1张蓝1
扫码查看

作者信息

  • 1. 华南农业大学数学与信息学院,广东 广州 510642
  • 折叠

摘要

设A(G)和D(G)分别表示图G的邻接矩阵和度对角矩阵,称Aα(G)=αD(G)+(1-α)A(G)为图G的Aα-矩阵,并称Aα(G)的最大特征值为图G的Aα-谱半径,其中α ∈[0,1).图G的Aα-矩阵是图G的邻接矩阵和无符号Laplacian矩阵的共同推广.该文研究了树的补图中谱半径的排序问题,分别确定了最大度为△的n阶树的补图中Aα-谱半径的唯一极大和唯一极小图,还确定了n阶树的补图中唯一的Aα-谱半径极小图.在此基础上,得到了n阶树的补图中邻接谱半径的标尺定理(The Scalar Theorem).

Abstract

Let A(G)and D(G)denote the adjacency matrix and the diagonal matrix of the degrees of a simple graph G,respectively.For α ∈[0,1),let Aα(G)=αD(G)+(1-α)A(G)be the Aα-matrix of the graph G,and the largest eigenvalue of Aα-matrix is called the Aα-spectral radius of G.The Aα-matrix of a graph G is a unified definition of the adjacency matrix and the signless Laplacian matrix of G.In this paper,the unique maximal and unique minimal extremal graph in the class of the complement graphs of trees with n vertices and maximum degree Δ is determined,respectively.Consequently,the unique minimal graph in the class of the complement graphs of trees with n vertices is also determined.The Scalar Theorem of spectral radius in the class of the complement graphs of trees with n vertices is proved.

关键词

Aα-矩阵/谱半径/树/补图/标尺定理(The/Scalar/Theorem)

Key words

Aα-matrix/spectral radius/trees/complement of graph/The Scalar Theorem

引用本文复制引用

出版年

2024
高校应用数学学报
浙江大学 中国工业与应用数学学会

高校应用数学学报

CSTPCD北大核心
影响因子：0.396
ISSN：1000-4424
段落导航相关论文