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2-Disjoint-path-coverable panconnectedness of crossed cubes

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Abstract

The crossed cube is a popular network topology because it possesses many attractive topological properties and its diameter is about half that of the hypercube. Typically, a network topology is modeled as a graph whose vertices and edges represent processors and communication links, respectively. We define a graph \(G\) to be \(2\)-disjoint-path-coverably \(r\)-panconnected for a positive integer \(r\) if for any four distinct vertices \(u,\, v,\, x\), and \(y\) of \(G\), there exist two vertex-disjoint paths \(P_1\) and \(P_2,\) such that (i) \(P_1\) joins \(u\) and \(v\) with length \(l\) for any integer \(l\) satisfying \(r \le l \le |V(G)| - r - 2\), and (ii) \(P_2\) joins \(x\) and \(y\) with length \(|V(G)| - l - 2\), where \(|V(G)|\) is the total number of vertices in \(G\). This property can be considered as an extension of both panconnectedness and connectivity. In this paper, we prove that the \(n\)-dimensional crossed cube is \(2\)-disjoint-path-coverably \(n\)-panconnected.

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Acknowledgments

This work was supported in part by the National Science Council of the Republic of China under Contracts NSC 99-2221-E-167-025 and NSC 98-2218-E-468-001-MY3.

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Authors and Affiliations

  1. Department of Information Management, National Chin-Yi University of Technology, Taiping, Taichung, 411, Taiwan

    Hon-Chan Chen

  2. Department of Computer Science and Information Engineering, Asia University, Wufeng, Taichung, 413, Taiwan

    Tzu-Liang Kung

  3. Department of Architecture, China University of Science and Technology, Nangang, Taipei, 115, Taiwan

    Li-Yen Hsu

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  1. Hon-Chan Chen
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  2. Tzu-Liang Kung
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  3. Li-Yen Hsu
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Correspondence to Hon-Chan Chen.

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Chen, HC., Kung, TL. & Hsu, LY. 2-Disjoint-path-coverable panconnectedness of crossed cubes. J Supercomput 71, 2767–2782 (2015). https://doi.org/10.1007/s11227-015-1417-9

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  • DOI: https://doi.org/10.1007/s11227-015-1417-9

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