The Fault-tolerant Pancyclicity And Panconnectivity Of The Folded Hypercubes

In this paper we study the fault-tolerant pancyclicity and panconnectivity of thefolded hypercubes. We proof that, if there exist 2ⁿ - 4 fault elements(vertices and/oredges) in n-dimension folded hypercubes,and each vertex incident with at least twofault-free edges, then there exist fault-free cycles of length at least 2ⁿ - 2ff_v,and that,if there exist 2ⁿ - 5 fault edges in n-dimension folded hypercubes,and each vertexincident with at least two fault-free edges,then for any two vertices u and v,there existfault-free uv-paths of length l for every l with dFQn(u,v) + 4≤l≤2ⁿ -- 1 andl - d_FQn(u,v)≡0(mod2).