Let G be a connected graph. Let \(t_1\geqslant 3\) , \(t_2\geqslant 3\) be two integers with \(t_1\leqslant t_2\) . Then G is two-disjoint-cycle-cover \([t_1,t_2]\) -pancyclic or briefly 2-DCC \([t_1,t_2]\) -pancyclic if for any integer t with \(t_1\leqslant t\leqslant t_2\) , G has two cycles \(C_1\) and \(C_2\) satisfying \(\vert V(C_1)\vert =t\) and \(V(C_2)=V(G)-V(C_1)\) . Let \(q,w\in V(G)\) with \(q\ne w\) be two arbitrary vertices. Then G is 2-DCC vertex \([t_1,t_2]\) -pancyclic if for any integer t with \(t_1\leqslant t\leqslant t_2\) , G has two cycles \(C_1,C_2\) such that \(q\in V(C_1), w\in V(C_2)\) , where \(\vert V(C_1)\vert =t\) , \(V(C_2)=V(G)-V(C_1)\) . We show that (n, 1)-star graph \(S_{n,1}\) is 2-DCC edge \([3,\lfloor \frac{n}{2}\rfloor ]\) -pancyclic, 2-DCC vertex \([3,\lfloor \frac{n}{2}\rfloor ]\) -pancyclic and 2-DCC \([3,\lfloor \frac{n}{2}\rfloor ]\) -pancyclic when \(n\geqslant 6\) . We obtain that (n, k)-star graph \(S_{n,k}\) is 2-DCC \([3, \frac{n!}{2(n-k)!}]\) -pancyclic when \(n\geqslant 8\) and \(2 \leqslant k \leqslant n-6.\)
