无符号拉普拉斯谱半径与图的哈密尔顿性  

Signless Laplacian Spectral Radius and Hamiltonicity

作　　者：何焕 王礼想 叶淼林 HE Huan;WANG Lixiang;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）》2023年第2期31-34,共4页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11871077);安徽省自然科学基金项目(1808085MA04);安徽省高校自然科学基金项目(KJ2020A0894,KJ2021A0650)。

摘　　要：在结构图论中,图的哈密尔顿性的谱刻画是最具有影响力的课题之一,其主要思想是判断一个图是不是哈密尔顿图,这是NP-完全问题。因此,诸多学者对哈密尔顿性问题的研究主要集中在寻找适当的充分条件。本文借助补图的无符号拉普拉斯谱半径来刻画具有较大最小度的图的哈密尔顿性。首先,采用反证法构造了原图的闭包,将原图是否具有某性质转化到其闭包中;其次对闭包补图的结构进行了合理的分类讨论;最后分别给出了具有较大最小度的图G是哈密尔顿的,哈密尔顿-连通的以及从任意点出发可迹的关于无符号拉普拉斯谱半径的充分条件。In structural graph theory,the spectrum characterization of Hamiltonicity of graphs has significant implica-tions.Judging whether a graph is a Hamiltonian graph is a NP-complete problem.Therefore,researchers focus on finding ap-propriate sufficient conditions for the Hamiltonicity problem.In this paper,the Hamiltonian property of graphs with large mini-mum degree is characterized by the signless Laplacian spectral radius of complementary graphs.Firstly,the closure of the orig-inal graph is constructed by contradiction evidence method,and whether the original graph has a certain property is trans-formed into its closure.Secondly,the structure of the closure complement is reasonably classified and discussed.Finally,the sufficient conditions on the signless Laplacian spectral radius that the graph with large minimum degree is Hamiltonian,Ham-ilton-connected and traceable from every vertex are given.

关 键 词：无符号拉普拉斯谱半径 哈密尔顿-连通 哈密尔顿 可迹 最小度 

分 类 号：O157.5[理学—数学]