不含悬挂点的双圈图及三圈图的谱半径
The Spectral Radius of Bicyclic and Tricyclic Graphs with no Pendant
张子杰 1蔡改香1
作者信息
- 1. 安庆师范大学数理学院,安徽安庆 246133
- 折叠
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.
Abstract
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.
关键词
无符号拉普拉斯谱半径/双圈图/三圈图Key words
signless Laplacian spectral radius/bicyclic graph/tricyclic graph引用本文复制引用
基金项目
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(KJ2021A0650)
出版年
2024
NETL
NSTL
万方数据