Partial domination - the isolation number of a graph

We prove the following result: If $G$ be a connected graph on $n\ge 6$ vertices, then there exists a set of vertices $D$ with $\mathrm{\mid }D\mathrm{\mid }\le \frac{n}{3}$ and such that $V(G)\setminus N[D]$ is an independent set, where $N[D]$ is the closed neighborhood of $D$. Furthermore, the bound is sharp. This seems to be the first result in the direction of partial domination with constrained structure on the graph induced by the non-dominated vertices, which we further elaborate in this paper.