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 beenproposed, however, this paper aims to show that when the network has a faulty vertex, a cycle can embed in it. Let $f$ 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 $2^n-2$, and if $n$ and $k$ have different parity, then $Q_{n,k}-{f}$ contains afaulty-free cycle of every even length from 4 to $2^n-2$ and every odd length from $n-k+2$ to $2^n-1$.
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机译：最近，已经调查了许多HyperCube的变体。在本文中，我们主要将注意力集中在更加超级的网络上，增强的超立方体。 N $ -dimensional增强型HyperCube，由$ Q_ {n，k} $表示，拥有许多优于超特性的属性。许多增强超级性的特性已经存在，但是，本文旨在表明，当网络有一个故障的顶点时，可以将一个循环嵌入其中。让$ f $是$ n $ -dimensional增强的超立体$ q_ {n，k} $的缺陷顶点，如果$ n $和$ k $有相同的奇偶校验，那么$ q_ {n，k} - {f} $包含从4到$ 2 ^ n-2 $的每一个均匀长周期，如果$ n $和$ k $有不同的奇偶校验，那么$ q_ {n，k} - {f} $包含apaulty-从4到$ 2 ^ n-2 $的自由循环每一个甚至的长度，每一个奇数长度到$ n-k + 2 $ 2 $ 2 ^ n-1 $。
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