Document Type

Article

Publication Date

1-1-2019

Journal / Book Title

IEEE Access

Abstract

We present new results on the fault tolerability of $k$-ary $n$-cube (denoted $Q{n}{k}$ ) networks. $Q{n}{k}$ is a topological model for interconnection networks that has been extensively studied since proposed, and this paper is concerned with the structure/substructure connectivity of $Q{n}{k}$ networks, for paths and cycles, two basic yet important network structures. Let $G$ be a connected graph and $T$ a connected subgraph of $G$. The $T$-structure connectivity $\kappa (G; T)$ of $G$ is the cardinality of a minimum set of subgraphs in $G$ , such that each subgraph is isomorphic to $T$ , and the set's removal disconnects $G$. The $T$-substructure connectivity $\kappa {s}(G; T)$ of $G$ is the cardinality of a minimum set of subgraphs in $G$ , such that each subgraph is isomorphic to a connected subgraph of $T$ , and the set's removal disconnects $G$. In this paper, we study $\kappa (Q{n}{k}; T)$ and $\kappa {s}(Q{n}{k}; T)$ for $T=P{i}$ , a path on $i$ nodes (resp. $T=C{i}$ , a cycle on $i$ nodes). Lv et al. determined $\kappa (Q{n}{k}; T)$ and $\kappa {s}(Q{n}{k}; T)$ for $T\in \{P{1},P{2},P{3}\}$. Our results generalize the preceding results by determining $\kappa (Q{n}{k}; P{i})$ and $\kappa {s}(Q{n}{k}; P{i})$. In addition, we have also established $\kappa (Q{n}{k}; C{i})$ and $\kappa {s}(Q{n}{k}; C{i})$.

DOI

10.1109/ACCESS.2019.2941711

Rights

This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see http://creativecommons.org/licenses/by/4.0/

Published Citation

Zhang, G., & Wang, D. (2019). Structure connectivity and substructure connectivity of $ k $-ary $ n $-cube networks. IEEE Access, 7, 134496-134504.

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