巢湖学院学报 ›› 2022, Vol. 24 ›› Issue (3): 52-55.doi: 10.12152/j.issn.1672-2868.2022.03.007

• 数理科学 • 上一篇    下一篇

无符号拉普拉斯谱半径与图的若干性质

刘莉,袁慧,何焕:安庆师范大学 数理学院   

  1. 安庆师范大学 数理学院,安徽 安庆 246133
  • 收稿日期:2021-11-25 出版日期:2022-05-25 发布日期:2022-09-06
  • 作者简介:刘莉(1997—),女,安徽安庆人,安庆师范大学数理学院硕士研究生,主要从事代数图论研究。
  • 基金资助:
    国家自然科学基金项目(项目编号:11871077);安徽省自然科学基金项目(项目编号:1808085MA04);安徽省高校自然科学基金项目(项目编号:KJ2020A0894);安徽高校自然科学研究重点项目(项目编号:KJ2021A0650);安徽高校研究生科学研究项目(项目编号:YJS20210515)

Signless Laplacian Spectral Radius and Some Properties of Graphs

LIU Li,YUAN Hui,HE Huan:School of Mathematics and Physics, Anqing Normal University   

  1. School of Mathematics and Physics, Anqing Normal University, Anqing Anhui 246133
  • Received:2021-11-25 Online:2022-05-25 Published:2022-09-06

摘要: 对于给定的简单图G,如何判断图G具有某种结构性质,这一问题一直广受图论学者们的青睐。由于图的谱能够很好地反映图的结构性质且便于计算,近年来,诸多学者利用图谱理论来研究图的相关性质。首先找到了原图对应结构性质的稳定性,其次构造原图的对应闭包,最后利用反证法,根据补图的无符号拉普拉斯谱半径分别给出了具有较大最小度的图Gs-连通、s-边-连通、s-路-覆盖、s-哈密尔顿、s-边-哈密尔顿、s-哈密尔顿-连通或α(G)≤s的充分条件。

关键词: 无符号拉普拉斯谱半径, 稳定性, 闭包, 最小度

Abstract: For any given simple graph G, the question of how to judge whether it has some structural properties has been explored by graph theory scholars. Because the spectrum of a graph can well reflect the structural properties of a graph and is easy for calculation, in recent years, many scholars have used the spectrum theory to study the related properties of a graph. In this paper, we first find the stability of the corresponding structural properties of graphs, then construct the corresponding closures of graphs; finally, by using the method of reductio ad absurdum, according to the signless Laplacian spectral radius of its complement, graph G with larger minimum degrees is the sufficient condition for s-connected, s-edge-connected, s-path-coverable, s-Hamiltonian, s-edge-Hamiltonian, s-Hamilton-connected or α(G)≤s.

Key words: signless Laplacian spectral radius, stability, closure, minimum degree

中图分类号: 

  • O157.5