  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 $\textrm{str}_{f}\left( G\right)$ of a numbering
$f:V\left( G\right) \rightarrow \left\{ 1,2,\ldots ,n\right\} $ of $G$ is
defined by% \begin{equation*} \mathrm{str}_{f}\left( G\right) =\max \left\{
f\left( u\right) +f\left( v\right) \left| uv\in E\left( G\right) \right.
\right\} \text{,} \end{equation*}% that is, $\mathrm{str}_{f}\left( G\right) $
is the maximum edge label of $G$ and the strength\ \textrm{str}$\left( G\right)
$ of a graph $G$ itself is \begin{equation*} \mathrm{str}\left( G\right) =\min
\left\{ \mathrm{str}_{f}\left( G\right) \left| f\text{ is a numbering of
}G\right. \right\} \text{.} \end{equation*} In this paper, we present a sharp
lower bound for the strength of a graph in terms of its domination number as
well as its (edge) covering and (edge) independence number. We also provide a
necessary and sufficient condition for the strength of a graph to attain the
earlier bound in terms of their subgraph structure. In addition, we establish a
sharp lower bound for the domination number of a graph under certain
conditions.
