带有最小度的哈密尔顿图的充分条件  

On Sufficient Conditions for Hamiltonian Graphs with Minimum Degree

作　　者：余桂东 袁慧 张子杰 YU Guidong;YUAN Hui;ZHANG Zijie(School of Mathematics and Physics,Anqing Normal University,Anqing Anhui 246133,China;Department of Public Teaching,Hefei preschool education college,Hefei Anhui 230013,China)

机构地区：[1]安庆师范大学数理学院,安徽安庆246133 [2]合肥幼儿师范高等专科学校公共教学部,安徽合肥230013

出　　处：《安徽理工大学学报（自然科学版）》2022年第5期71-74,共4页Journal of Anhui University of Science and Technology:Natural Science

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(YJ2020A0894,YJ20210650);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：由于图的谱能够很好地反映图的结构性质且便于计算,因而可以利用图谱理论来研究图的哈密尔顿性。主要研究哈密尔顿图的谱充分条件和无符号拉普拉斯谱充分条件。首先介绍图的闭包性质;然后对图的闭包结构进行分析、论证,利用度序列以及反证法找出带有最小度的图是哈密尔顿图的边数充分条件;最后根据图的边数与谱半径、无符号拉普拉斯谱半径的关系,分别给出G是哈密尔顿图的谱充分条件、无符号拉普拉斯谱充分条件。所得到的结论均优化已有结论。Since the spectrum of a graph reflects well the structural properties of a graph and is easy to calculate,the spectrum theory is usually used to study the Hamiltonian property of a graph i.e.the spectral sufficient conditions and signless Laplacian spectral sufficient conditions of Hamiltonian graphs.In the research the closure property of graphs wasintroduced and the structure of the closure of the graph was reasonably analyzed and demonstrated and then the edge number sufficient condition for the graph with minimum degree was found being Hamiltonian by using degree sequence and contradiction.Finally,according the relation between edge number and the(signless Laplacian)spectral radius of the graph,the spectral sufficient conditions and signlessLaplacian spectral sufficient conditions of Hamiltonian graphs were given respectively.All the conclusions achieved are better than the existing conclusions.

关 键 词：最小度 哈密尔顿图 谱半径 无符号拉普拉斯谱半径 

分 类 号：O157.5[理学—数学]