Cluster Connectivity And Super Cluster Connectivity Of DQcube. (23rd December 2021)

• Record Type: Journal Article
• Authors: Zhou, Qianru; Zhou, Shuming; Liu, Xiaoqing; Yu, Zhengqin
• Is Part Of: Computer journal. Volume 66:Number 4(2023)
• Page Start: 826
• Page End: 841
• Publication Date: 2021-12-23
• Subjects: Interconnection networks -- DQcube -- Cluster connectivity -- Super cluster connectivity; Computers -- Periodicals; 005.1
• DOI: 10.1093/comjnl/bxab198
• Languages: English
• ISSNs: 0010-4620

Abstract

Abstract: As a fundamental metric, the connectivity to assess fault tolerance and reliability of interconnection networks has been extensively explored. However, classical connectivity is not very effective at evaluating large-scale networking systems. To overcome this deficiency, two new indices, cluster connectivity and super cluster connectivity, have been proposed to characterize the robustness of interconnection networks. This paper focuses on investigating $\mathcal{H} (\mathcal{H}^{*})$ -cluster connectivity and super $\mathcal{H} (\mathcal{H}^{*})$ -connectivity of composition graph $DQ_{n}$, based on disc-ring and hypercube, for $\mathcal{H}\in \{K_{1, r}\ |\ 0\leq r\leq n+1\}$, respectively. In detail, we show that $\kappa (DQ_{n}|K_{1, 1} (K_{1, 1}^{*}))=\kappa ^{\prime}(DQ_{n}|K_{1, 1}(K_{1, 1}^{*})) =n+1 (n\geq 3)$, $\kappa (DQ_{n}|K_{1, r}(K_{1, r}^{*})) =\left\lceil \frac{n}{2}\right\rceil +1 (2\leq r\leq 4)$ for $n\geq 3$, $\kappa ^{\prime}(DQ_{n}|K_{1}(K_{1}^{*})) =\kappa ^{\prime}(DQ_{n})=2n (n\geq 3)$, and for $2\leq r\leq 3$ and $k\geq 2$, $$\begin{align*} \kappa^{\prime}(DQ_{n}|K_{1, r}(K_{1, r}^{*}))=\left\{\begin{array}{@{}ll} n+1, & if\ n=2k+1; \\ n, & if\ n=2k. \end{array}\right. \end{align*}$$ As by-products, we show that DQcube is super $K_{1, r}-\ (K_{1, r}^{*}-)$ connected $(2\leq r\leq 3)$, and derive the 4-extra connectivity of DQcube $\kappa _{4}(DQ_{n}) = 5n-9 (n\geq 4)$ .