  Let $G=(V,E)$ be a graph. A subset $D\subseteq V$ is a dominating set if
every vertex not in $D$ is adjacent to a vertex in $D$. A dominating set $D$ is
called a total dominating set if every vertex in $D$ is adjacent to a vertex in
$D$. The domination (resp. total domination) number of $G$ is the smallest
cardinality of a dominating (resp. total dominating) set of $G$. The bondage
(resp. total bondage) number of a nonempty graph $G$ is the smallest number of
edges whose removal from $G$ results in a graph with larger domination (resp.
total domination) number of $G$. The reinforcement number of $G$ is the
smallest number of edges whose addition to $G$ results in a graph with smaller
domination number. This paper shows that the decision problems for bondage,
total bondage and reinforcement are all NP-hard.
