给定连通度和独立数图的最大A_(α)谱半径  

Maximum A_(α) spectral radius of graphs with given the connectivity and independence number

作　　者：张磊 韩淑蓉[1] 余欢 周曾鹏 ZHANG Lei;HAN Shu-rong;YU Huan;ZHOU Zeng-peng(College of Mathematics and Statistics,Qinghai Normal University,Xining 810016,China;The State Key Laboratory of Tibetan Information Processing and Application,Qinghai Normal University,Xining 810016,China)

机构地区：[1]青海师范大学数学与统计学院,青海西宁810016 [2]青海师范大学省部共建藏文智能信息处理及应用国家重点实验室,青海西宁810016

出　　处：《青海师范大学学报（自然科学版）》2023年第1期48-51,共4页Journal of Qinghai Normal University(Natural Science Edition)

基　　金：青海省自然科学基金资助项目(2022-ZJ-973Q);青海师范大学本科生科技创新项目(qhnuxskj 2021047)

摘　　要：令A(G)、D(G)分别是图G的邻接矩阵和度矩阵,对于任意实数α∈[0,1],图G的A_(α)矩阵记作:A_(α)(G)=αD(G)+(1-α)A(G).对于图G,如果图G至少有k+2个顶点,且删除任意k-1个顶点后图依然是连通图,那么图G是k-连通的,连通度记作k.独立集是图G中任意互不相邻的顶点的集合,最大的独立集是给定图G中一个顶点数最多的独立集,而这个最大独立集的顶点个数就是图G的独立数,记作r.在本文中我们主要研究n阶、连通性为k、独立数为r的图类,我们确定了这类图具有最大A_(α)谱半径的极图结构.Let G be a graph with adjacency matrix A(G),and let D(G)be the diagonal matrix of the degrees of G.For any realα∈[0,1],write A_(α)for the matrix A_(α)(G)=αD(G)+(1-α)A(G).For a graph,the graph has at least k+2vertices,and the graph is still connected after deleting any k-1vertices,then the connectivity of the graph is k.The independent set is the set of vertices that are not adjacent to each other.The largest independent set is the independent set with the largest number of vertices in a given graph,and the cardinality of the largest independent set is the independent number of the graph,written as r.In this paper we focus on maximum A_(α)spectral radius of graphs with given the order connectivity minimum degree and independence number.We determine the graphs in this family that have the maximumA_(α)-spectral radius.

关 键 词：图 A_(α)谱半径 独立数 连通度 

分 类 号：O212.1[理学—概率论与数理统计]