Some results on topological properties of folded hypercubes

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