图的最小特征值  

The least eigenvalue of the graph

作　　者：高润霞[1,2] 余桂东 蔡改香 Gao Runxia;Yu Guidong;Cai Gaixiang(Department of Social Undertakings,Anqing Vocational and Technical College,Anqing 246133,China;School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆职业技术学院,安徽安庆246133 [2]安庆师范大学数理学院,安徽安庆246133

出　　处：《纯粹数学与应用数学》2022年第4期482-486,共5页Pure and Applied Mathematics

基　　金：国家自然科学基金(11371028);安徽省教育厅自然科学基金(11371028,KJ2016A447).

摘　　要：设图G是一个简单图,G的邻接矩阵用A(G)表示,A(G)的最小特征值λ(G)被称为G的最小特征值.首先建立了图的邻接矩阵的边数与最小特征值之间的关系,然后给出具有Hamiltonian路径或Hamiltonian圈的一些谱条件,或是Hamilton连通的,或是从每个顶点追踪到图的邻接矩阵的最小特征值.这为研究图的结构性质提供了一种行之有效的方法.Let G be a simple graph.The adjacency matrix is denoted by G.The least eigenvalue of A(G),denoted byλ(G),is called the least eigenvalue of G.In this paper we?rst establish the relations between the number of edges and the least eigenvalue of the adjacency matrix of the graph,and then give some spectral conditions for a graph having Hamiltonian paths or Hamiltonian cycles,or being Hamilton-connected,or being traceable from every vertex in terms of the least eigenvalue of the adjacency matrix of the graph.This provides an effiective method for us to study some properties for a graph.

关 键 词：最小特征值 HAMILTON路 HAMILTON圈 Hamilton连通图 

分 类 号：O157.5[理学—数学]