strong domination number of a modified graph

Let g = (v,e) be a simple graph. a set d ⊆ v is a strong dominating set of g, if for every vertex x ∈ v d there is a vertex y ∈ d with xy ∈ e(g) and deg(x) ≤ deg(y). the strong domination number γst(g) is defined as the minimum cardinality of a strong dominating set. in this paper, we study the effects on γst(g) when g is modified by operations on vertices and edges of g.