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A novel edge connectivity based on edge partition for hypercube and folded hypercube

Author

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  • Chen, Meirun
  • Habib, Michel
  • Lin, Cheng-Kuan

Abstract

Edge connectivity is often used to capture edge fault tolerance. As for most common networks, their edge connectivity is exactly equal to their minimum degree. Edge matroidal connectivity and conditional edge matroidal connectivity are two new graph edge connectivity parameters that can be defined when a partition of the edge set is given, for example when the network is built with different kinds of edges having different expected faultiness. And those two edge connectivity parameters can measure edge fault tolerance more than the traditional definition. The edge matroidal connectivity is based on the associated edge partition and the other is a generalization called conditional edge matroidal connectivity. We analyze these new parameters on hypercubes and folded hypercubes which are well studied networks. In this study, we consider their standard dimensional partition of the edges. This study leads to more structural insights about edge connectivity and yields many interesting questions.

Suggested Citation

  • Chen, Meirun & Habib, Michel & Lin, Cheng-Kuan, 2024. "A novel edge connectivity based on edge partition for hypercube and folded hypercube," Applied Mathematics and Computation, Elsevier, vol. 470(C).
    • Handle: RePEc:eee:apmaco:v:470:y:2024:i:c:s0096300324000304
    DOI: 10.1016/j.amc.2024.128558
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    References listed on IDEAS

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    1. Liu, Xuemei & Meng, Jixiang, 2021. "The k-restricted edge-connectivity of the data center network DCell," Applied Mathematics and Computation, Elsevier, vol. 396(C).
    2. Balbuena, C. & Marcote, X., 2019. "The p-restricted edge-connectivity of Kneser graphs," Applied Mathematics and Computation, Elsevier, vol. 343(C), pages 258-267.
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