论文标题
在Ky Fan $ k $ -li $ -matrix的图形上
On the Ky Fan $k$-norm of the $LI$-matrix of graphs
论文作者
论文摘要
令$ a（g）$和$ d（g）$分别为图$ g $的邻接矩阵和对角矩阵。然后$ l（g）= d（g）-a（g）$称为图$ g $的拉普拉斯矩阵。让$ g $是$ n $顶点和$ m $边缘的图。然后，$ g $的$ li $ -matrix定义为$ li（g）= l（g） - \ frac {2m} {n} i_n $，其中$ i_n $是身份矩阵。在本文中，我们对$ li $ $ $ -matrix的ky fan fan $ k $ norm的极端特性感兴趣，该属性与众所周知的问题和结果图中的结果密切相关，例如laplacian光谱半径，laplacian，laplacian，$ k $ k $ k $ k $ k $ k $ k $ k $ k $ k $ laplacian laplacian eigenvalues and laplacues，laplac and laplac，laplace and laplac。给出了$ li $ -matrix的ky fan $ k $ norm上的一些界限，并部分表征了极端图。此外，确定了$ li $ -matrix的Ky Fan Fan $ K $ norm上的上限和下限，确定了树木，单环图和双环图，并表征了相应的极端图。
Let $A(G)$ and $D(G)$ be the adjacency matrix and the degree diagonal matrix of a graph $G$, respectively. Then $L(G)=D(G)-A(G)$ is called Laplacian matrix of the graph $G$. Let $G$ be a graph with $n$ vertices and $m$ edges. Then the $LI$-matrix of $G$ are defined as $LI(G)=L(G)-\frac{2m}{n}I_n$, where $I_n$ is the identity matrix. In this paper, we are interested in extremal properties of the Ky Fan $k$-norm of the $LI$-matrix of graphs, which is closely related to the well known problems and results in spectral graph theory, such as the Laplacian spectral radius, the Laplacian spread, the sum of the $k$ largest Laplacian eigenvalues, the Laplacian energy, and other parameters. Some bounds on the Ky Fan $k$-norm of the $LI$-matrix of graphs are given, and the extremal graphs are partly characterized. In addition, upper and lower bounds on the Ky Fan $k$-norm of $LI$-matrix of trees, unicyclic graphs and bicyclic graphs are determined, and the corresponding extremal graphs are characterized.
