摘要
无符号拉普拉斯谱研究的目的是通过分析图像或数据的频域特征来实现特定任务。图的顶点度矩阵与邻接矩阵的和称为无符号拉普拉斯矩阵,连通图的无符号拉普拉斯矩阵是非负不可约矩阵,其最大特征值被称为无符号拉普拉斯谱半径。满足边数与顶点数差为1的图被称为双圈图,边数与顶点数差为2的图被称为三圈图。图谱问题一直是图论中的热点研究问题,文章分别确定了所有不含悬挂点的双圈图及三圈图的图类中具有最大无符号拉普拉斯谱半径的图的结构。
The sum of the diagonal degree matrix and the adjacency matrix of the graph is called the signless Laplacian matrix,and the signless Laplacian matrix of the connected graph is a non-negative irreducible matrix,and its largest eigenvalue is called the signless Laplacian spectral radius.A graph that satisfies a difference of 1 between the number of edges and vertices is called a Bicyclic graph,and a graph that has a difference of 2 from the number of edges and vertices is called a Tricyclic graph.The spectral problem has always been ahot research problem in graph theory.In this paper,we deter-mine the structure of graphs with maximum signless Laplacian spectral radius in the class of Bicyclic graph and Tricyclic graph with no pendant,respectively.
作者
张子杰
蔡改香
ZHANG Zijie;CAI Gaixiang(School of Mathematics and Physics,Anqing Normal University,Anqing 246133,Anhui,China)
出处
《合肥学院学报（综合版）》
2024年第2期15-21,27,共8页
Journal of Hefei University：Comprehensive ED
基金
安徽省研究生线下课程“图论”(2022xxsfkc038)
安徽省高校自然科学研究重点项目“图的哈密尔顿性与基于距离的拓扑指数研究”(KJ2021A0650)。
关键词
无符号拉普拉斯谱半径
双圈图
三圈图
signless Laplacian spectral radius
bicyclic graph
tricyclic graph
作者简介
张子杰(1998-),男,安徽合肥人,硕士研究生,研究方向:代数图论,E-mail:1455899391@qq.com;蔡改香(1981-),女,安徽庐江人,副教授,研究方向:代数图论。
