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Super \(K_{1,p}\)-Connectivity of Locally Twisted Cubes

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Innovative Mobile and Internet Services in Ubiquitous Computing (IMIS 2022)

Part of the book series: Lecture Notes in Networks and Systems ((LNNS,volume 496))

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Abstract

Interconnection networks are emerging as an approach to solving system-level communication problems. A network is abstractly modeled by a graph. For \(p \ge 1\), a p-star \(K_{1,p}\) includes \(p+1\) nodes such that a single node (called center) is linked to each of the other p nodes. The connectivity has long been a classic factor that characterizes both network reliability and fault tolerance. A set F of node subsets of G is a \(K_{1,p}\)-cut if \(G-F\) is disconnected, and each element of F happens to induce a p-star in G. A super \(K_{1,p}\)-cut F of G is a \(K_{1,p}\)-cut in G such that the smallest component of \(G-F\) contains two or more nodes. Then the super \(K_{1,p}\)-connectivity of G, denoted by \(\kappa '(G|K_{1,p})\), is the cardinality of the minimum super \(K_{1,p}\)-cut of G. The locally twisted cube \(LTQ_n\) is a promising alternative to the hypercube and can serve as the backbone architecture of high-performance computing. In this article, we are inspired to determine \(\kappa '(LTQ_n|K_{1,p})\) for \(p=1,2,3\).

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Acknowledgements

This work is supported in part by the Ministry of Science and Technology, Taiwan, under Grant No. MOST 109-2221-E-468-009-MY2.

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Authors and Affiliations

  1. Department of Computer Science and Information Engineering, Providence University, Taichung City, Taiwan

    Yuan-Hsiang Teng

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

    Tzu-Liang Kung

Authors
  1. Yuan-Hsiang Teng
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  2. Tzu-Liang Kung
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Correspondence to Tzu-Liang Kung .

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Editors and Affiliations

  1. Department of Information and Communication Engineering, Fukuoka Institute of Technology, Fukuoka, Japan

    Leonard Barolli

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Teng, YH., Kung, TL. (2022). Super \(K_{1,p}\)-Connectivity of Locally Twisted Cubes. In: Barolli, L. (eds) Innovative Mobile and Internet Services in Ubiquitous Computing. IMIS 2022. Lecture Notes in Networks and Systems, vol 496. Springer, Cham. https://doi.org/10.1007/978-3-031-08819-3_27

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