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The n-dimensional enhanced hypercube \(Q_{n,k}(1 \leq k \leq n-1 )\) is one of the most attractive interconnection networks for parallel and distributed computing system. Let \(H\) be a certain particular connected subgraph of graph \(G\). The \(H\)-structure-connectivity of \(G\), denoted by \(\kappa (G;H),\) is the cardinality of minimal set of subgraphs \(F=\{H_1,H_2,…,H_m\}\) in \(G\) such that every \(H_i\in F\) is isomprphic to \(H\) and \(G-F\) is disconnected. The \(H\)-substructure-connectivity of \(G\), denoted by \(_k^3(G;H)\), is the cardinality of minimal set of subgraphs \(F={H_1,H_2,…,H_m}\) in \(G\) such that every \(H_i\in F\) is isomorphic to a connected subgraph \(H\) , and \(G-F\) is disconnected. Using the structural properties of \(Q_{n,k}\) the \(H\)-structure-connectivity \(\kappa (Q_{n,k};H)\) were determine for \(H \in \{K_1,K_{1,1},K_{1,2},K_{1,3}\}\).