Some results on topological properties of folded hypercubes

An n-dimensional folded hypercube FQn is an attractive variance of an n-dimensional hypercube Qn, it is obtained by adding an edge between every pair of vertices with complementary addresses. Recently, Hsieh studied edge-fault-tolerant Hamiltonicity of FQn, and Fang studied (bi)panconnectivity of FQn. In this paper, we first give a result on the connection between FQn and Qn, then applying known topological properties of hypercubes, we improve the results of Hsieh; also, we obtain some results on fault-tolerant (bi)panconnectivity of FQn that generalize the results of Fang. By our method it is possible to obtain other topological properties of FQn.