Cycles in Conditional Faulty Enhanced Hypercube Networks
The architecture of an interconnection network is usually represented by a graph, and a graph G is bipancyclic if it contains a cycle for every even length from 4 to vertical bar V(G)vertical bar. In this article, we analyze the conditional edge-fault-tolerant properties of an enhanced hypercube, which is an attractive variant of a hypercube that can be obtained by adding some complementary edges. For any n-dimensional enhanced hypercube with at most (2n - 3) faulty edges in which each vertex is incident with at least two fault-free edges, we showed that there exists a fault-free cycle for every even length from 4 to 2(n) when n (n >= 3) and k have the same parity. We also show that a fault-free cycle for every odd length exists from n - k + 2 to 2(n) - 1 when n (n >= 2) and k have the different parity.
cycle enhanced hypercube embedding fault-tolerant