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- W4308393497 abstract "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." @default.
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- W4308393497 date "2020-12-21" @default.
- W4308393497 modified "2023-09-23" @default.
- W4308393497 title "On the Ky Fan $k$-norm of the $LI$-matrix of graphs" @default.
- W4308393497 doi "https://doi.org/10.48550/arxiv.2012.11162" @default.
- W4308393497 hasPublicationYear "2020" @default.
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