论文标题
在具有一些归一化的Laplacian特征值的图表上
On graphs with some normalized Laplacian eigenvalue of extremal multiplicity
论文作者
论文摘要
令$ g $为$ n $顶点上的连接简单图。令$ \ mathcal {l}（g）$为$ g $的归一化laplacian矩阵，$ρ_{n-1}（g）$是$ \ mathcal {l}（l}（g）$的第二个最小特征。用$ν（g）$表示$ g $的独立数。最近，该论文[具有某些归一化laplacian特征值的图表$ n-3 $，arxiv：1912.13227]与某些归一化的laplacian特征值$ n-3 $讨论了图形。但是，剩下的情况（$ρ_{n-1}（g）\ neq 1 $和$ν（g）= 2 $的图形不考虑。在本文中，我们专注于直径3的Cophaphs和图形，以研究具有多重性$ n-3 $的一些归一化laplacian特征值的图形。
Let $G$ be a connected simple graph on $n$ vertices. Let $\mathcal{L}(G)$ be the normalized Laplacian matrix of $G$ and $ρ_{n-1}(G)$ be the second least eigenvalue of $\mathcal{L}(G)$. Denote by $ν(G)$ the independence number of $G$. Recently, the paper [Characterization of graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$, arXiv:1912.13227] discussed the graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$. However, there is one remaining case (graphs with $ρ_{n-1}(G)\neq 1$ and $ν(G)= 2$) not considered. In this paper, we focus on cographs and graphs with diameter 3 to investigate the graphs with some normalized Laplacian eigenvalue of multiplicity $n-3$.
