图的哈密尔顿性的A_(α)-谱条件  

Aα-Spectral Conditions for Hamiltonicity of Graphs

作　　者：何焕 叶淼林 HE Huan;YE Miaolin(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《安庆师范大学学报（自然科学版）》2022年第3期37-41,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11871077);安徽省自然科学基金(1808085MA04);安徽省高校自然科学研究重点项目(KJ2020A0894,KJ2021A0650);安徽高校研究生科学研究项目(YJS20210515)。

摘　　要：判断给定的图是不是哈密尔顿图是一个重要的NP-完全问题。图的谱理论就是研究如何通过一些容易计算的不变量来描述图的性质,它是代数图论和组合矩阵论的一个十分重要的研究领域。本文将A_(α)-谱半径和图的哈密尔顿性联系在一起,分别给出了具有最小度数条件的连通图是哈密尔顿-连通的、哈密尔顿的、可迹的谱充分条件。研究目的在于推广无符号拉普拉斯谱半径到A_(α)-谱半径,进而讨论图的哈密尔顿性,以此建立图的拓扑结构。It is an important NP-complete problem to determine whether a given graph is a Hamilton graph.The spectrum theory of graphs is to study how to describe the properties of graphs by some easily calculated invariants,which is a very im-portant research field in algebraic graph theory and combinatorial matrix theory.In this paper,we combine the Aα-spectral radi-us with the hamiltonicity of graphs,and give the sufficient spectral conditions for the connected graphs with the minimum de-gree condition to be Hamilton-connected,hamiltonian and traceable.The purpose of this study is to extend the signless Lapla-cian spectral radius to Aα-spectral radius,and then discuss the hamiltonicity of graphs,so as to establish the topological struc-ture of graphs.

关 键 词：A_(α)-谱半径 连通图 最小度 哈密尔顿性 

分 类 号：O157.5[理学—数学]