哈密尔顿图的谱半径条件  

Spectral Radius Condition of Hamiltonian Graph

作　　者：方怡 谢欣宇 钱王晟 Fang Yi;Xie Xinyu;Qian Wangsheng(Tongling Polytechnic,Tongling 244061,China;Anqing Normal University,Anqing 246133,China)

机构地区：[1]铜陵职业技术学院,安徽铜陵244061 [2]安庆师范大学,安徽安庆246133

出　　处：《廊坊师范学院学报（自然科学版）》2024年第3期30-32,36,共4页Journal of Langfang Normal University(Natural Science Edition)

基　　金：国家自然科学基金(11871077);安徽省高校科学研究重点项目“图的哈密尔顿性研究”(2023AH052887);省级研究生线下示范课程图论(2022xxsfkc038);校级研究生线下课程图论(2021aqnuxxkc03);院级质量工程教学研究重点项目(tlpt2023jyzd006)。

摘　　要：设G是一个简单图,G的邻接矩阵是表示G顶点之间相邻关系的矩阵,它的最大特征值被定义为图的谱半径。一个包含图G中所有顶点的圈称为哈密尔顿圈,如果图G包含一个哈密尔顿圈,则称图G是哈密尔顿图。设G具有最小度条件,主要利用G的谱半径给出G是哈密尔顿图的充分条件。Let G be a simple graph.The adjacency matrix of G is the one which represents adjacent relation between vertices of G,the largest eigenvalue of the adjacency matrix of which is called the spectral radius of G.A Hamiltonian cycle of G is a cycle which contains all vertices of G.The graph G is called Hamiltonian graph if it contains a Hamiltonian cycle.Let G have minimum degree condition,and this paper mainly studies some conditions for G to be a Hamiltonian graph in terms of the spectral radius.

关 键 词：连通图 哈密尔顿图 谱半径 最小度 

分 类 号：O157.5[理学—数学]