%0 Journal Article
%T On the strength and independence number of powers of paths and cycles
%J Communications in Combinatorics and Optimization
%I Azarbaijan Shahid Madani University
%Z 2538-2128
%A Ichishima, Rikio
%A Muntaner Batle, Francisco Antonio
%A Takahashi, Yukio
%D 2024
%\ 03/17/2024
%V
%N
%P -
%! On the strength and independence number of powers of paths and cycles
%K strength
%K independence number
%K $k$th power of a graph
%K graph labeling
%K combinatorial optimization
%R 10.22049/cco.2024.29087.1839
%X 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.
%U https://comb-opt.azaruniv.ac.ir/article_14720_64c90a09bab45be62e744bcdc10e4680.pdf