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 Fbe the set of faulty vertices in the n-dimensional enhanced hypercube Q(1 ≤ k≤n- 1).When |F| = 2,we showed that Q-Fcontains a fault-free cycle of every even length from 4 to 2~n- 4 where n(n ≥ 3) and fc have the same parity;and contains a fault-free cycle of every even length from 4 to 2~n- 4,simultaneously,contains a cycle of every odd length from n — fc + 2 to 2~n-3 where n(≥ 3) and fc 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~n- 2fwhether n(n > 3) and fe have the same parity or not;and there exists the longest fault-free cycle,which is of odd length 2~n-2f- 1 in Q— Fwhere n(≥ 3) and fc have the different parity.