哈密尔顿图的谱充分条件  

Sufficient Conditions for Hamiltonian Graphs in Terms of Spectral Radius

作　　者：许秋晨 叶淼林 XU Qiuchen;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42-46,共5页Journal of Anqing Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11871107);安徽省高校自然科学基金(KJ2017A362)。

摘　　要：图的谱半径和无符号拉普拉斯谱半径在研究图的结构和性质中发挥着重要作用。本文从边条件出发,通过计算得出度序列并刻画其对应的图形,进而对这些满足给定边条件的图是否为哈密尔顿图进行了研究,在此基础上把图的谱半径、无符号拉普拉斯谱半径与边条件联系在一起,对图的哈密尔顿性的充分条件进行了探讨。通过边条件和谱条件探讨图的哈密尔顿性是研究图哈密尔顿性的一种可行、有效的方法。The spectral radius and the signless Laplacian spectral radius of graphs play an important role in studying the structural properties of graphs.In the paper,starting from the edge conditions,the degree sequence is calculated and the corre-sponding graphs are characterized,and then the graphs satisfying the edge conditions are studied whether they are hamiltonian graphs.On this basis,the spectral radius and the signless Laplacian spectral radius of graphs are connected with boundary con-ditions,and the sufficient conditions for hamiltonian property of graphs are discussed.It is a feasible and effective method to study the hamiltonian property of graphs by using boundary conditions and spectral conditions.

关 键 词：边条件 谱半径 无符号拉普拉斯谱半径 哈密尔顿性 

分 类 号：O157.5[理学—数学]