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h-Restricted H-structure connectivity and h-restricted H-substructure connectivity of hypercube

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Abstract

The connectivity of a network is an important indicator to its reliability and fault tolerability. Since the faulty elements in the network may have some special structures, two new kinds of conditional connectivity, called h-restricted H-structure connectivity and h-restricted H-substructure connectivity, are proposed as a generalization of conditional connectivity, where \(h\ge 1\), and H is some special structure. In this paper, we establish both h-restricted H-structure connectivity and h-restricted H-substructure connectivity for the hypercube \(Q_n\), where the special structures are \(K_1, K_{1,1}, K_{1,2}\), respectively.

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Data Availability Statement

No data, models, or code were generated or used during the study.

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Acknowledgements

The authors would like to express their gratitude to the editor and the anonymous referees for their valuable suggestions about this paper. This research was supported by Zhejiang Provincial Natural Science Foundation of China under Grant No.LQ18F020004, the State Administration for Market Regulation Technical Support Special Project under Grant No.2021YJ006, and National Key Research and Development Plan “NQI Integrated Services Common Technologies Research” special project under Grant No 2021YFF0600100.

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Authors and Affiliations

  1. Key Laboratory of Electromagnetic Wave Information Technology and Metrology of Zhejiang Province, College of Information Engineering, China Jiliang University, Hangzhou, 310018, China

    Cui Yu, Fei Gao & Boyong Gao

  2. Department of Computer Science, University of Otago, Dunedin, 9016, New Zealand

    Yawen Chen

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  1. Cui Yu
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  2. Fei Gao
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Correspondence to Boyong Gao.

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Yu, C., Gao, F., Gao, B. et al. h-Restricted H-structure connectivity and h-restricted H-substructure connectivity of hypercube. J Supercomput 79, 8499–8512 (2023). https://doi.org/10.1007/s11227-022-04983-6

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  • DOI: https://doi.org/10.1007/s11227-022-04983-6

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