Fault-tolerant Panconnectivity Of Hypercubes

In this paper,we study the fault-tolerant panconnectivity of hypercubes and augmented cubes.We prove that,if there exist at most 2n-5 fault edges in an n-dimension hypercube,for any two distinct vertices u and(?)there exists a fault-free uv-path of length e for every e with d(u,v)+4≤e≤2~n-1 and e-d(u,v)≡0(mod2),and that,if there exist at most 2n-5 fault elements(vertices and/or edges)in an n-dimension augmented cube,for any two distinct vertices u and v,there exists a fault-free uv-path of length e for every e with d(u,v)+2≤2≤e≤2~n-f-1.where d(u,v)denotes the distance between two vertices u and v in the network.and f is the number of fanlt vertices.