Journal of Communications and Networks

The Korean Institute of Commucations and Information Sciences (한국통신학회)
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Cycles in Conditional Faulty Enhanced Hypercube Networks

  • Liu, Min (College of Science, China Three Gorges University) ;
  • Liu, Hongmei (College of Science, China Three Gorges University)
  • Received : 2011.01.26
  • Accepted : 2011.06.27
  • Published : 2012.04.30
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Abstract

The architecture of an interconnection network is usually represented by a graph, and a graph G is bipancyclic if it contains a cycle for every even length from 4 to ${\mid}V(G){\mid}$. In this article, we analyze the conditional edge-fault-tolerant properties of an enhanced hypercube, which is an attractive variant of a hypercube that can be obtained by adding some complementary edges. For any n-dimensional enhanced hypercube with at most (2n-3) faulty edges in which each vertex is incident with at least two fault-free edges, we showed that there exists a fault-free cycle for every even length from 4 to $2^n$ when n($n{\geq}3$) and k have the same parity. We also show that a fault-free cycle for every odd length exists from n-k+2 to $2^n-1$ when n($n{\geq}2$) and k have the different parity.

Keywords

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