具有固定匹配数的单圈图的A_(∝)-谱半径  

On A_(∝)-spectral radius of unicyclic graphs with fixed mathing number

作　　者：李梦霞 房明磊 LI Meng-xia;FANG Ming-lei(School of Mathematics and Big Data,Anhui University of Science and Technology,Huainan 232001,China)

机构地区：[1]安徽理工大学数学与大数据学院,安徽淮南232001

出　　处：《哈尔滨商业大学学报（自然科学版）》2023年第2期200-203,227,共5页Journal of Harbin University of Commerce：Natural Sciences Edition

基　　金：国家自然科学基金(No.12171190);安徽省自然科学基金(No.2008085MA01)。

摘　　要：对于任意的α∈[0,1],Nikiforov提出了矩阵A_(α)(G)=αD(G)+(1-α)A(G),记为图G的A_(α)-矩阵,其中A(G)是G的邻接矩阵,D(G)是G的度对角矩阵.矩阵A_(α)(G)的最大特征值称为图G的A_(α)-谱半径.考虑固定匹配数的所有单圈图,确定了前三个具有最大A_(α)-谱半径的图.For any realα∈[0,1],Nikiforov proposed the matrix A_(α)(G)=αD(G)+(1-α)A(G),which was the A_(α)-matrix of a graph G,where A(G)was the adjacency matrix of G and D(G)was the diagonal matrix of the degrees of G.In this paper,the first three graphs with the largest A_(α)-spectral radius among all unicyclic graphs with fixed matching number were determined.

关 键 词：单圈图 树 A_(α)-谱半径 最大特征值 匹配数 邻接矩阵 

分 类 号：O157.5[理学—数学]