福州大学学报（自然科学版）2026，Vol.54Issue(2)：123-128,6.DOI:10.7631/issn.1000-2243.25031
图的Aα谱半径的两个新界
Two new bounds for the Aα spectral radius of graphs
摘要
Abstract
This study focuses on the problem of the upper and lower bounds of the Aα spectral radius for any simple graphs.First,based on the structural properties of cliques in graphs and the concept of average vertex degree,combined with classical inequalities and some matrix-theory methods,we derive a novel lower bound for the Aα spectral radius of simple graphs.Then,through the matrices of line graph and the relationships between a graph and its line graph,and introducing the concept of average 2-degree of vertices in the graph,we further derive a novel upper bound for the Aα spectral radius of simple graphs.Finally,by comparing with some known upper and lower bounds of the Aα spectral radius of graphs,we conduct in-depth discussions from both theoretical analysis and specific examples to demonstrate the superiority of the new bounds.关键词
Aα谱半径/上下界/平均二度/团Key words
Aα spectral radius/upper and lower bounds/average 2-degree/clique分类
数理科学引用本文复制引用
刘剑萍,刘曙光..图的Aα谱半径的两个新界[J].福州大学学报（自然科学版）,2026,54(2):123-128,6.基金项目
国家自然科学基金资助项目(12171089) （12171089）
