Total isolation of k-cliques in a graph

For a graph $G=\left(V\right(G),E(G\left)\right)$ and any positive integer k, a set $D\subseteq V\left(G\right)$ is called a total k-clique isolating set of G if $G-N\left[D\right]$ contains no k-clique and D induces a subgraph with no vertex of degree 0. The total k-clique isolation number ${\iota }_t(G,k)$ is the minimum cardinality of a total k-clique isolating set of G. Clearly, ${\iota }_t(G,1)$ is the total domination number of G, and ${\iota }_t(G,2)$ was investigated by Boyer, Goddard and Henning recently. In this paper, we prove that for $k\ge 3$ and $n\ge k+2$, if G is a connected graph of order n, then ${\iota }_t(G,k)\le \frac{2n}{k+2}$. The bound is sharp.