تقرير
A complete solution of the $k$-uniform supertrees with the eight largest $\alpha$-spectral radii
| العنوان: | A complete solution of the $k$-uniform supertrees with the eight largest $\alpha$-spectral radii |
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| المؤلفون: | Yu, Lou-Jun, Wang, Wen-Huan |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | Let $\mathcal T (n, k)$ be the set of the $k$-uniform supertrees with $n$ vertices and $m$ edges, where $k\geq 3$, $n\geq 5$ and $m=\frac{n-1}{k-1}$. % Let $m$ be the number of the edges of the supertrees in $\mathcal T (n, k)$, where $m=\frac{n-1}{k-1}$. A conjecture concerning the supertrees with the fourth through the eighth largest $\alpha$-spectral radii in $\mathcal T (n, k)$ was proposed by You et al.\ (2020), where $0 \leq \alpha<1$, $k\geq 3$ and $m \geq 10$. This conjecture was partially solved for $1-\frac{1}{m-2}\leq \alpha <1$ and $m\geq 10$ by Wang et al.\ (2022). When $0\leq \alpha <1-\frac{1}{m-2}$ and $m \geq 10$, whether this conjecture is correct or not remains a problem to be further solved. By using a new $\rho_{\alpha}$-normal labeling method proposed in this article for computing the $\alpha$-spectral radius of the $k$-uniform hypergraphs, we completely prove that this conjecture is right for $0\leq\alpha<1$ and $m\geq 13$. Comment: 21 pages,1 figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2308.00422 |
| رقم الأكسشن: | edsarx.2308.00422 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |