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Let $G=(V,E)$ be a graph. A set $S\subseteq V(G)$ is a dominating set, ifevery 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 whosevertices 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 correspondingdominating sets of $G$ differ by either adding or deleting a single vertex. Inthis paper we consider and study the $n$-dominating graph of specific graphs.

On the $n-$dominating graph of specific graphs