拟平衡二部图的弱逐点可迹性的若干充分条件  

Some Sufficient Conditions forWeak Vertex-by-Vertex Traceability of Quasi-Balanced Bipartite Graphs

作　　者：刘莉 余桂东 袁慧 LIU Li;YU Guidong;YUAN Hui(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20-26,共7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);安徽省高校自然科学研究重点项目(KJ2021A0650);安徽高校研究生科学研究项目(YJS20210515)。

摘　　要：图的哈密尔顿问题一直以来都是图论研究的重点和难点。由于图的谱和拓扑指数便于计算,近年来人们开始利用其优势来研究图的哈密尔顿性。受此启发,首先根据平衡二部图是弱哈密尔顿-连通的边充分条件得到拟平衡二部图是弱逐点可迹的边充分条件;其次利用图的谱半径及无符号拉普拉斯谱半径分别给出了拟平衡二部图是弱逐点可迹的充分条件;最后利用图的Wiener指数、Hyper-Wiener指数以及Harary指数分别给出了拟平衡二部图是弱逐点可迹的充分条件。The Hamiltonian problem in graph theory has always been a challenging focus of study.In recent years,re-searchers have used the spectrum and topological index as easily calculable values to explore the Hamiltonian of graphs.In-spired by this,firstly,according to the edge sufficient condition that the balanced bipartite graph is weakly Hamiltonian-con-nected,the edge sufficient condition that the quasi-balanced bipartite graph is weakly traceable vertex by vertex is obtained.Secondly,the sufficient conditions for the quasi-balanced bipartite graph to be weakly traceable vertex by vertex are given by using the spectral radius or the signless Laplace spectral radius of the graph.Finally,by using the Wiener index,Hyper-Wiener index and Harary index of graphs,the sufficient conditions for the quasi-balanced bipartite graph to be weakly traceable vertex by vertex are given respectively.

关 键 词：拟平衡二部图 弱逐点可迹 谱半径 无符号拉普拉斯谱半径 拓扑指数 

分 类 号：O157.5[理学—数学]