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On conditional diagnosability and reliability of the BC networks

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Abstract

An n-dimensional bijective connection network (in brief, BC network), denoted by X n , is an n-regular graph with 2n nodes and n2n−1 edges. Hypercubes, crossed cubes, twisted cubes, and Möbius cubes all belong to the class of BC networks (Fan and He in Chin. J. Comput. 26(1):84–90, [2003]). We prove that the super connectivity of X n is 2n−2 for n≥3 and the conditional diagnosability of X n is 4n−7 for n≥5. As a corollary of this result, we obtain the super connectivity and conditional diagnosability of the hypercubes, twisted cubes, crossed cubes, and Möbius cubes.

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  1. Department of Mathematics, Xidian University, Xi’an, Shaanxi, 710071, China

    Qiang Zhu

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  1. Qiang Zhu
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Correspondence to Qiang Zhu.

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Zhu, Q. On conditional diagnosability and reliability of the BC networks. J Supercomput 45, 173–184 (2008). https://doi.org/10.1007/s11227-007-0167-8

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  • DOI: https://doi.org/10.1007/s11227-007-0167-8

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