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On the strength and independence number of powers of paths and cycles | ||
| Communications in Combinatorics and Optimization | ||
| مقاله 1، دوره 10، شماره 4، اسفند 2025، صفحه 717-728 اصل مقاله (371.58 K) | ||
| نوع مقاله: Original paper | ||
| شناسه دیجیتال (DOI): 10.22049/cco.2024.29087.1839 | ||
| نویسندگان | ||
| Rikio Ichishima* 1؛ Francisco Antonio Muntaner-Batle2؛ Yukio Takahashi3 | ||
| 1Department of Sport and Physical Education, Faculty of Physical Education, Kokushikan University, 7-3-1 Nagayama, Tama-shi, Tokyo 206-8515, Japan | ||
| 2Graph Theory and Applications Research Group, School of Electrical Engineering and Computer Science, Faculty of Engineering and Built Environment, The University of Newcastle, NSW 2308, Australia | ||
| 3Department of Science and Engineering, Faculty of Electronics and Informatics, Kokushikan University, 4-28-1 Setagaya, Setagaya-ku, Tokyo 154-8515, Japan | ||
| چکیده | ||
| A numbering $f$ of a graph $G$ of order $n$ is a labeling that assigns distinct elements of the set $\left\{1,2, \ldots, n \right\}$ to the vertices of $G$. The strength $\mathrm{str}\left(G\right) $ of $G$ is defined by $\mathrm{str}\left( G\right) =\min \left\{ \mathrm{str}_{f}\left( G\right)\left\vert f\text{ is a numbering of }G\right. \right\}$, where $\mathrm{str}_{f}\left( G\right) =\max \left\{ f\left( u\right)+f\left( v\right) \left\vert uv\in E\left( G\right) \right. \right\} $. Using the concept of independence number of a graph, we determine formulas for the strength of powers of paths and cycles. To achieve the latter result, we establish a sharp upper bound for the strength of a graph in terms of its order and independence number and a formula for the independence number of powers of cycles. | ||
| کلیدواژهها | ||
| strength؛ independence number؛ $k$th power of a graph؛ graph labeling؛ combinatorial optimization | ||
| مراجع | ||
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