The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs

Zhang, Yanhong; Zhang, Lei; Ren, Haizhen

doi:10.22108/toc.2025.143292.2221

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	The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs
Transactions on Combinatorics
دوره 15، شماره 2، شهریور 2026، صفحه 125-136 اصل مقاله (507.2 K)
نوع مقاله: Research Paper
شناسه دیجیتال (DOI): 10.22108/toc.2025.143292.2221
نویسندگان
Yanhong Zhang؛ Lei Zhang؛ Haizhen Ren^*
Department of Mathematics and Statistics, Qinghai Normal University, Xining, China
چکیده
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.].
کلیدواژه‌ها
Graph؛ Integer $k$-matching؛ Distance Laplacian؛ Spectral radius

مراجع
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The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs