Let \( {\mathcal {H}} \) be a connected subgraph of a graph G. The \({\mathcal {H}}\) -structure connectivity of G, denoted by \( \kappa (G;{\mathcal {H}}) \) , is the minimum cardinality of a set of connected subgraphs in G, whose removal either disconnects G or reduces it to a trivial graph, where each element in the set is isomorphic to \( {\mathcal {H}} \) . The \({\mathcal {H}}\) -substructure connectivity of G, denoted by \( \kappa ^s(G;{\mathcal {H}}) \) , is the minimum cardinality of a set of connected subgraphs in G, whose removal either disconnects G or reduces it to a trivial graph, where each element in the set is isomorphic to a connected subgraph of \( {\mathcal {H}} \) . In this paper, we investigate the \( {\mathcal {H}} \) -structure connectivity and \( {\mathcal {H}} \) -substructure connectivity of folded divide-and-swap cube \( FDSC_n \) for \( {\mathcal {H}}\in \{K_1, K_{1,1}, K_{1,m} \text (2\le m \le d+2) \} \) where \( n=2^d \) . We show that \(\kappa (FDSC_n;K_1)=\kappa ^s(FDSC_n;K_1)=d+2\) , \(\kappa (FDSC_n;K_{1,1})=\kappa ^s(FDSC_n;K_{1,1})=d+1 \) for \( d\ge 3 \) and \(\kappa (FDSC_n;K_{1,m})=\kappa ^s(FDSC_n;K_{1,m})=\lfloor \frac{d}{2}\rfloor +1\) for \(d\ge 1 \) and \( 2\le m \le d+1\) . Moreover, we show that \(\kappa ^s(FDSC_n;K_{1,d+2})=\lfloor \frac{d}{2}\rfloor +1\) for \(d\ge 1 \) and we provide a bound for \(\kappa (FDSC_n;K_{1,d+2})\) when \(d\ge 3 \) .
