Generalized measures of fault tolerance in exchanged hypercubes

  • Authors:
  • Xiang-Jun Li;Jun-Ming Xu

  • Affiliations:
  • School of Mathematical Sciences, University of Science and Technology of China, Wentsun Wu Key Laboratory of CAS, Hefei, 230026, China and School of Information and Mathematics, Yangtze University ...;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

The exchanged hypercube EH(s,t), proposed by Loh et al. [P.K.K. Loh, W.J. Hsu, Y. Pan, The exchanged hypercube, IEEE Transactions on Parallel and Distributed Systems 16 (9) (2005) 866-874], is obtained by removing edges from a hypercube Q"s"+"t"+"1. This paper considers a kind of generalized measures @k^(^h^) and @l^(^h^) of fault tolerance in EH(s,t) with 1@?s@?t and determines @k^(^h^)(EH(s,t))=@l^(^h^)(EH(s,t))=2^h(s+1-h) for any h with 0@?h@?s. The results show that at least 2^h(s+1-h) vertices (resp. 2^h(s+1-h) edges) of EH(s,t) have to be removed to get a disconnected graph that contains no vertices of degree less than h, and generalizes some known results.