Azarbaijan Shahid Madani UniversityCommunications in Combinatorics and Optimization2538-2128Articles in Press20240317On the strength and independence number of powers of paths and cycles1472010.22049/cco.2024.29087.1839ENRikio IchishimaDepartment of Sport and Physical Education, Faculty of Physical Education, Kokushikan UniversityFrancisco Antonio Muntaner BatleThe University of NewcastleYukio TakahashiDepartment of Electronics and Informatics, School of Science and Engineering, Kokushikan UniversityJournal Article20231024A 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\} $.<br />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.https://comb-opt.azaruniv.ac.ir/article_14720_64c90a09bab45be62e744bcdc10e4680.pdf