图的Aα谱半径的两个新界OA
Two new bounds for the Aα spectral radius of graphs
研究任意简单图的 Aα 谱半径的上下界问题.首先,基于图中团的结构特性以及顶点平均度的概念,结合一些经典不等式和矩阵论方法,推导出任意简单图的 Aα 谱半径的一个新下界.然后,通过分析线图矩阵、图与其线图之间的内在关系,并引入图中顶点的平均二度概念,进一步推导出任意简单图的 Aα 谱半径的一个新上界.最后,通过与图的一些已知 Aα 谱半径的上下界进行比较,从理论分析和具体实例两个层面深入探讨,展示新界的优越性.
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.
刘剑萍;刘曙光
福州大学数学与统计学院,福建 福州 350108福州大学数学与统计学院,福建 福州 350108
数理科学
Aα谱半径上下界平均二度团
Aα spectral radiusupper and lower boundsaverage 2-degreeclique
《福州大学学报（自然科学版）》 2026 (2)
123-128,6
国家自然科学基金资助项目(12171089)
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