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article · IEEE Access · 2019

Reliability Assessment of Hierarchical Hypercube Networks

Shu-Li Zhao, Rong‐Xia Hao

Cited by 9Open access

Abstract

The g-good neighbor connectivity κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (G) and g-good-neighbor diagnosability t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (G) are two important parameters to evaluate the reliability and fault tolerance for an interconnection network G. So far, almost all known results about κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (G) and t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (G) are about special g except the hypercubes, the star graphs, the k-ary n-cubes, and so on. In this paper, we focus on κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) and t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) for the n-dimensional hierarchical hypercube network HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> for 1 ≤ g ≤ m - 1 and m ≥ 2, where n = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">m</sup> + m. We show that κ <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (m + 1 - g) for 1 ≤ g ≤ m - 1. In addition, we show that t <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sub> (HHC <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">n</sub> ) = 2 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">g</sup> (m + 2 - g) - 1 under the PMC model and MM* model for 1 ≤ g ≤ m - 1.

Cite this paper

APA 7

Zhao, S.-L., & Hao, R. (2019). Reliability Assessment of Hierarchical Hypercube Networks. IEEE Access, 7, 54015–54023. https://doi.org/10.1109/access.2019.2912014

MLA 9

Zhao, Shu-Li, and Rong‐Xia Hao. “Reliability Assessment of Hierarchical Hypercube Networks.” IEEE Access, vol. 7, 2019, pp. 54015–23, https://doi.org/10.1109/access.2019.2912014.

Chicago

Zhao, Shu-Li, and Rong‐Xia Hao. 2019. “Reliability Assessment of Hierarchical Hypercube Networks.” IEEE Access 7: 54015–23. https://doi.org/10.1109/access.2019.2912014.

Harvard

Zhao, S.-L. and Hao, R. (2019) ‘Reliability Assessment of Hierarchical Hypercube Networks’, IEEE Access, 7, pp. 54015–54023. Available at: https://doi.org/10.1109/access.2019.2912014.

BibTeX
@article{zhao2019reliability,
  title = {{Reliability Assessment of Hierarchical Hypercube Networks}},
  author = {Zhao, Shu-Li and Hao, Rong‐Xia},
  journal = {IEEE Access},
  volume = {7},
  pages = {54015--54023},
  year = {2019},
  doi = {10.1109/access.2019.2912014}
}

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