Vertex-Fault-Tolerant Cycles Embedding on Enhanced Hypercube

Recently, many variants of hypercube have been investigated. In this article, we mainly focus our attention on a more hypercube-like network, the enhanced hypercube. The n-dimensional enhanced hypercube, denoted by Q_n,k, possesses many properties superior to the hypercube. Many properties of enhanced hypercube have been proposed, however, this paper aims to show that when the network has a faulty vertex, a cycle can embed in it. Let / be a faulty vertex in n-dimensional enhanced hypercube Q_n,k, if n and k have the same parity, then Q_n,k - {f} contains a faulty-free cycle of every even length from 4 to 2n - 2, and if n and k have different parity, then Q_n,k - {f} contains a faulty-free cycle of every even length from 4 to 2ⁿ-2 and every odd length from n-k + 2 to 2ⁿ - 1.