k 连通非正则图的 A_(α) 谱半径  

The A_(α) Spectral Radius of k- connected Irregular Graphs

作　　者：李翔宇 张海霞[1] LI Xiang-yu;ZHANG Hai-xia(School of Applied Sciences,Taiyuan University of Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应用科学学院,太原030024

出　　处：《太原科技大学学报》2024年第5期520-525,共6页Journal of Taiyuan University of Science and Technology

基　　金：山西省自然科学基金(202103021224284)。

摘　　要：设G为n个顶点m条边的k连通非正则图,图G的A_(α)矩阵[1]定义为A_(α)(G)=αD(G)+(1-α)A(G),0≤α≤1.其中D(G)和A(G)分别为图G的度对角矩阵和邻接矩阵,利用图的最大度Δ和最小度δ得到了图G的A_(α)谱半径ρ_(α)的一个上界。此外,还确定了k连通Δ正则图的子图的A_(α)谱半径的上界。Let G be a k-connected irregular graph with n vertices,m edges.Defined the matrix A_(α)(G)as A_(α)(G)=αD(G)+(1-α)A(G),0≤α≤1.Where D(G)and A(G)are degree diagonal matrix and adjacency matrix of G.In this paper,give an upper bound of the A_(α)spectral radius of the graph G in terms of maximum degreeΔand minimum degreeδ,and also determine the upper bound of the A_(α)spectral radius of the subgraphs of k-connectedΔregular graph.

关 键 词：A_(α)矩阵 A_(α)谱半径 非正则图 k连通图 

分 类 号：O157.5[理学—数学]