Department of Mathematics and Statistics, Qinghai Normal University, Xining, China
10.22108/toc.2025.143292.2221
Abstract
Let $G$ be a graph with order $n$. Aouchiche and Hansen first proposed the distance Laplacian matrix of $G$, defined as $\mathcal{L}(G)=diag(Tr)-\mathcal{D}(G)$, where $\mathcal{D}(G)$ is the distance matrix and $diag(Tr)=diag(Tr(v_1),Tr(v_2),\ldots,Tr(v_n))$ is the diagonal matrix of the vertex transmissions of $G$, and the largest eigenvalue of $\mathcal{L}(G)$ is called the distance Laplacian spectral radius of $G$, written as $\rho_{\mathcal{L}}(G)$. By using the equitable quotient matrix of $\mathcal{L}(G)$, Tutte Theorem and Tutte-Berge Formula of integer $k$-matching, we establish the lower bound for the distance Laplacian spectral radius of $G$ among all $n$-vertex graphs with given integer $k$-matching number and characterized the corresponding extremal graph. This generalizes the results of Wang et al. [Lower bounds of distance Laplacian spectral radii of $n$-vertex graphs in terms of matching number, Linear Algebra Appl. 506 (2016) 579-587.] and Liu et al. [Lower bounds of distance Laplacian spectral radii of $n$-vertex graphs in terms of fractional matching number, J. Oper. Res. Soc. China. (2023) 1-8.].
Zhang, Y. , Zhang, L. and Ren, H. (2025). The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs. Transactions on Combinatorics, (), -. doi: 10.22108/toc.2025.143292.2221
MLA
Zhang, Y. , , Zhang, L. , and Ren, H. . "The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs", Transactions on Combinatorics, , , 2025, -. doi: 10.22108/toc.2025.143292.2221
HARVARD
Zhang, Y., Zhang, L., Ren, H. (2025). 'The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs', Transactions on Combinatorics, (), pp. -. doi: 10.22108/toc.2025.143292.2221
CHICAGO
Y. Zhang , L. Zhang and H. Ren, "The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs," Transactions on Combinatorics, (2025): -, doi: 10.22108/toc.2025.143292.2221
VANCOUVER
Zhang, Y., Zhang, L., Ren, H. The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs. Transactions on Combinatorics, 2025; (): -. doi: 10.22108/toc.2025.143292.2221
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