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A note on median eigenvalues of subcubic graphs
| العنوان: | A note on median eigenvalues of subcubic graphs |
|---|---|
| المؤلفون: | Wang, Yuzhenni, Zhang, Xiao-Dong |
| المصدر: | Discrete Applied Mathematics, 2023 |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics, 05C50 |
| الوصف: | Let $G$ be an simple graph of order $n$ whose adjacency eigenvalues are $\lambda_1\ge\dots\ge\lambda_n$. The HL--index of $G$ is defined to be $R(G)= \max\{|\lambda_{h}|, |\lambda_{l}|\}$ with $h=\left\lfloor\frac{n+1}{2}\right\rfloor$ and $ l=\left\lceil\frac{n+1}{2}\right\rceil.$ Mohar conjectured that $R(G)\le 1$ for every planar subcubic graph $G$. In this note, we prove that Mohar's Conjecture holds for every $K_4$-minor-free subcubic graph. Note that a $K_4$-minor-free graph is also called a series--parallel graph. In addition, $R(G)\le 1$ for every subcubic graph $G$ which contains a subgraph $K_{2,3}$. Comment: 6 pages, 1figure |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2311.01884 |
| رقم الانضمام: | edsarx.2311.01884 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |