Analysis on the Component Connectivity of Enhanced Hypercubes
Analysis on the Component Connectivity of Enhanced Hypercubes
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DOI：
10.1093/comjnl/bxaa122
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发表时间：
2020-10
期刊：
影响因子：
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通讯作者：
Liqiong Xu;Litao Guo
中科院分区：
文献类型：
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作者：
Liqiong Xu;Litao Guo
互连网络的可靠性评估对互连网络的设计和维护具有重要意义。元件连通度是互连网络可靠性评估的一个重要参数，是传统连通度的推广。一个非完全连通图G的g-分支连通度c\kappa _g（G）是指删除G中至少有g个分支的顶点的最小数目。在许多互连网络中，确定g元连通度仍然是一个未解决的问题。设$Q_{n，k}$（$1\leq k\leq n-1$）表示$（n，k）$-增强超立方体。设$n\geq 7$和$1\leq k \leq n-5$，我们确定了$c\kappa _{g}（Q_{n，k}）= g（n + 1）- \frac{1}{2}g（g + 1）+ 1$，其中$2\leq g \leq n$。Zhao和Yang（2019，折叠超立方体的条件连通性。谨慎。应用数学，257，388-392）被延长。
Reliability evaluation of interconnection networks is of significant importance to the design and maintenance of interconnection networks. The component connectivity is an important parameter for the reliability evaluation of interconnection networks and is a generalization of the traditional connectivity. The $g$-component connectivity $c\kappa _g (G)$ of a non-complete connected graph $G$ is the minimum number of vertices whose deletion results in a graph with at least $g$ components. Determining the $g$-component connectivity is still an unsolved problem in many interconnection networks. Let $Q_{n,k}$ ($1\leq k\leq n-1$) denote the $(n, k)$-enhanced hypercube. In this paper, let $n\geq 7$ and $1\leq k \leq n-5$, we determine $c\kappa _{g}(Q_{n,k}) = g(n + 1) - \frac{1}{2}g(g + 1) + 1$ for $2 \leq g \leq n$. The previous result in Zhao and Yang (2019, Conditional connectivity of folded hypercubes. Discret. Appl. Math., 257, 388–392) is extended.