Vertex-fault-tolerant cycles embedding on enhanced hypercube networks.

In this paper, we focus on the vertex-fault-tolerant cycles embedding on enhanced hypercube, which is an attractive variant of hypercube and is obtained by adding some complementary edges from hypercube. Let F be the set of faulty vertices in the n-dimensional enhanced hypercube Q (1 ≤ k ≤ n−1). When | F | = 2, we showed that Q − F contains a fault-free cycle of every even length from 4 to 2 −4 where n ( n ≥ 3) and k have the same parity; and contains a fault-free cycle of every even length from 4 to 2 − 4, simultaneously, contains a cycle of every odd length from n − k + 2 to 2 − 3 where n(≥ 3) and k have the different parity. Furthermore, when | F | = f ≤ n − 2, we proof that there exists the longest fault-free cycle, which is of even length 2 − 2 f whether n( n ≥ 3) and k have the same parity or not; and there exists the longest fault-free cycle, which is of odd length 2 − 2 f − 1 in Q − F where n(≥ 3) and k have the different parity. [ABSTRACT FROM AUTHOR]