Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The extra connectivity is an important parameter for the reliability evaluation of interconnection networks and is a generalization of the traditional connectivity. Let $g\geq 0$ be an integer and $G$ be a connected graph; the $g$-extra connectivity of $G$ is the minimum cardinality of a set of vertices in $G$, if it exists, whose removal disconnects $G$ and leaves every component with more than $g$ vertices. Determining the $g$-extra connectivity is still an unsolved problem in many interconnection networks. Let $n$, $k$ be positive integers. Let $Q_{n,k}\, (1 \leq k \leq n-1)$ denote the $(n, k)$-enhanced hypercube. In this paper, we determine the $g$-extra connectivity of $Q_{n,k}$ is $(n+1)(g+1)-\frac{g(g+3)}{2}$ for $0\leq g\leq n-k-1$, $4\leq k\leq n-5\,(n\geq 9)$. Some previous results in [Zhang, M. and Zhou, J. (2015) On g-extra connectivity of folded hypercubes. Theor. Comput. Sci., 593, 146–153.] and [Sabir, E., Mamut, A. and Vumar, E. (2019) The extra connectivity of the enhanced hypercubes. Theor. Comput. Sci., 799, 22–31.] are extended.

中文翻译：

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论增强超立方体的g-Extra连通性

互连网络的可靠性评估对于互连网络的设计和维护具有重要意义。额外连通性是互连网络可靠性评估的重要参数，是传统连通性的推广。令$g\geq 0$ 为整数，$G$ 为连通图；$G$ 的 $g$-extra 连通性是 $G$ 中一组顶点的最小基数（如果存在），它的移除断开了 $G$ 并留下每个组件有超过 $g$ 个顶点。在许多互连网络中，确定 $g$-extra 连通性仍然是一个未解决的问题。令 $n$, $k$ 为正整数。令 $Q_{n,k}\, (1 \leq k \leq n-1)$ 表示 $(n, k)$ 增强的超立方体。在本文中，我们确定了 $Q_{n 的 $g$-extra 连通性，k}$ 是 $(n+1)(g+1)-\frac{g(g+3)}{2}$ 对于 $0\leq g\leq nk-1$, $4\leq k\leq n- 5\,(n\geq 9)$。[Zhang, M. 和 Zhou, J. (2015) 关于折叠超立方体的 g 额外连通性的一些先前结果。理论。计算。Sci., 593, 146–153.] 和 [Sabir, E., Mamut, A. 和 Vumar, E. (2019) 增强超立方体的额外连通性。理论。计算。Sci., 799, 22-31.] 已扩展。