On conditional diagnosability and reliability of the BC networks

  • Authors:
  • Qiang Zhu

  • Affiliations:
  • Department of Mathematics, Xidian University, Xi'an, China 710071

  • Venue:
  • The Journal of Supercomputing
  • Year:
  • 2008

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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 2 n nodes and n2 n驴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驴2 for n驴3 and the conditional diagnosability of X n is 4n驴7 for n驴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.