strong domination number of some operations on a graph

Let $g=(v(g),e(g))$ be a simple graph. a set $dsubseteq v(g)$ is a strong dominating set of $g$, if for every vertex $xin v(g)setminus d$ there is a vertex $yin d$ with $xyin e(g)$ 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 $g$.