  Let $G=(V,E)$ be a graph. A set $S\subseteq V(G)$ is a dominating set, if
every vertex in $V(G)\backslash S$ is adjacent to at least one vertex in $S$.
The $k$-dominating graph of $G$, $D_k (G)$, is defined to be the graph whose
vertices correspond to the dominating sets of $G$ that have cardinality at most
$k$. Two vertices in $D_k(G)$ are adjacent if and only if the corresponding
dominating sets of $G$ differ by either adding or deleting a single vertex. In
this paper we consider and study the $n$-dominating graph of specific graphs.
