  Let $G=(V(G),E(G))$ be a simple graph. A set $D\subseteq V(G)$ is a strong
dominating set of $G$, if for every vertex $x\in V(G)\setminus D$ there is a
vertex $y\in D$ with $xy\in E(G)$ and $deg(x)\leq deg(y)$. The strong
domination number $\gamma_{st}(G)$ is defined as the minimum cardinality of a
strong dominating set. In this paper, we examine the effects on
$\gamma_{st}(G)$ when $G$ is modified by operations on edge (or edges) of $G$.
