两类图的无符号拉普拉斯谱充分条件  

Signless Laplacian spectral conditions for two kinds of graphs

作　　者：王磊 蔡改香 WANG Lei;CAI Gaixiang(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,Anhui,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133

出　　处：《华中师范大学学报（自然科学版）》2022年第6期928-934,共7页Journal of Central China Normal University：Natural Sciences

基　　金：国家自然科学基金(11871077);安徽省自然科学基金(1808085MA04,1908085MC62);安徽省高校自然科学研究重点项目(KJ2020A0894,KJ2021A0650);安徽省高校研究生科学研究项目(YJS20210515);研究生线下课程《图论》(2021aqnuxxkc03).

摘　　要：该文研究了图的两种特殊性质,这两种特殊性质均具有稳定性.首先对原图进行了闭包运算并构造了原图的闭包,将原图是否具有某性质转化到了闭包补图中;其次对闭包补图的结构进行了合理的分类讨论;最后找到了在一定条件下当补图的无符号拉普拉斯谱半径不大于2k时,原图的独立数不超过k,或在一定条件下当补图的无符号拉普拉斯谱半径不大于n-2时,原图是哈密尔顿-连通的.Two special properties of graphs are studied in this paper.Both of these properties are stable.Firstly,the closure operation is carried out on the original graph and the closure of the original graph is constructed.Whether the original graph has some property is transformed into the complement of the closure.Secondly,the structure of the complement of closure is reasonably classified and discussed.Finally,it is found that under certain conditions the independent number of the original graph is no more than k when the signless Laplacian spectral radius of the complement is not greater than 2k,or under certain conditions,the original graph is Hamilton-connected when the signless Laplacian spectral radius of the complement is not greater than n-2.

关 键 词：无符号拉普拉斯谱半径 度序列 补图 稳定性 

分 类 号：O157.5[理学—数学]