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The relation between distance Laplacian spectral radius and integer $k$-matching number in graphs | ||
| Transactions on Combinatorics | ||
| مقالات آماده انتشار، پذیرفته شده، انتشار آنلاین از تاریخ 08 خرداد 1404 | ||
| 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 | ||
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آمار تعداد مشاهده مقاله: 22 |
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