Edge-fault tolerance of hypercube-like networks

  • Authors:

  • Xiang-Jun Li;Jun-Ming Xu

  • Affiliations:

  • School of Information and Mathematics, Yangtze University, Jingzhou, Hubei, 434023, China and School of Mathematical Sciences, University of Science and Technology of China, Wentsun Wu Key Laborat ...;School of Mathematical Sciences, University of Science and Technology of China, Wentsun Wu Key Laboratory of CAS, Hefei, 230026, China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2013

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Abstract

This paper considers a kind of generalized measure @l"s^(^h^) of fault tolerance in a hypercube-like graph G"n which contains several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes, crossed cubes, Mobius cubes and the recursive circulant G(2^n,4), and proves @l"s^(^h^)(G"n)=2^h(n-h) for any h with 0@?h@?n-1 by the induction on n and a new technique. This result shows that at least 2^h(n-h) edges of G"n have to be removed to get a disconnected graph that contains no vertices of degree less than h. Compared with previous results, this result enhances fault-tolerant ability of the above-mentioned networks theoretically.