تقرير
Bounds for eccentricity-based parameters of graphs
| العنوان: | Bounds for eccentricity-based parameters of graphs |
|---|---|
| المؤلفون: | Tang, Yunfang, Qi, Xuli, West, Douglas B. |
| سنة النشر: | 2023 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Combinatorics |
| الوصف: | The \emph{eccentricity} of a vertex $u$ in a graph $G$, denoted by $e_G(u)$, is the maximum distance from $u$ to other vertices in $G$. We study extremal problems for the average eccentricity and the first and second Zagreb eccentricity indices, denoted by $\sigma_0(G)$, $\sigma_1(G)$, and $\sigma_2(G)$, respectively. These are defined by $\sigma_0(G)=\frac{1}{|V(G)|}\sum_{u\in V(G)}e_G(u)$, $\sigma_1(G)=\sum_{u\in V(G)}e_G^2(u)$, and $\sigma_2(G)=\sum_{uv\in E(G)}e_G(u)e_G(v)$. We study lower and upper bounds on these parameters among $n$-vertex connected graphs with fixed diameter, chromatic number, clique number, or matching number. Most of the bounds are sharp, with the corresponding extremal graphs characterized. Comment: 27 pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2304.11537 |
| رقم الأكسشن: | edsarx.2304.11537 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |