论文标题
在具有远距离拉普拉斯特征值$ n-4 $的图表上
On graphs with distance Laplacian eigenvalues of multiplicity $n-4$
论文作者
论文摘要
令$ g $为带有$ n $顶点的连接简单图。距离拉普拉斯矩阵$ d^{l}（g）$定义为$ d^l（g）= diag（tr）-d（g）$，其中$ diag（tr）$是顶点传输的对角矩阵，$ d（g）$是$ g $ $ g $的距离矩阵。 $ d^{l}（g）$的特征值是$ g $的laplacian eigenvalues，并由$ \ partial_ {1}^{l}^{l}^{l}（G） \ partial_ {n}^{l}（g）$。最大的特征值$ \ partial_ {1}^{l}（g）$称为距离laplacian光谱半径。 Lu等。 （2017），Fernandes等。 （2018）和Ma等。 （2018年）完全表征了具有一定距离的Laplacian特征值$ n-3 $的图形。在本文中，我们将具有距离拉普拉斯频谱$ n-4 $的距离laplacian频谱半径以及距离laplacian特征值之一的图表为3或2的$ n $。此外，我们完全确定了距离laplacian laplacian eigenvalue $ n $ n $ n-4 $ n-4 $ n-4 $ n-4 $。
Let $G$ be a connected simple graph with $n$ vertices. The distance Laplacian matrix $D^{L}(G)$ is defined as $D^L(G)=Diag(Tr)-D(G)$, where $Diag(Tr)$ is the diagonal matrix of vertex transmissions and $D(G)$ is the distance matrix of $G$. The eigenvalues of $D^{L}(G)$ are the distance Laplacian eigenvalues of $G$ and are denoted by $\partial_{1}^{L}(G)\geq \partial_{2}^{L}(G)\geq \dots \geq \partial_{n}^{L}(G)$. The largest eigenvalue $\partial_{1}^{L}(G)$ is called the distance Laplacian spectral radius. Lu et al. (2017), Fernandes et al. (2018) and Ma et al. (2018) completely characterized the graphs having some distance Laplacian eigenvalue of multiplicity $n-3$. In this paper, we characterize the graphs having distance Laplacian spectral radius of multiplicity $n-4$ together with one of the distance Laplacian eigenvalue as $n$ of multiplicity either 3 or 2. Further, we completely determine the graphs for which the distance Laplacian eigenvalue $n$ is of multiplicity $n-4$.
