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Ninth International Conference on Parallel and Distributed Systems (ICPADS'02)
On the Fault-Tolerant Pancyclicity of Crossed Cubes
Taiwan, ROC
December 17-December 20
ISBN: 0-7695-1760-9
Wen-Tzeng Huang, National Taipei University of Technology
Woei-kae Chen, National Taipei University of Technology
Chin-Hsing Chen, Chungtai Institute of Health Sciences and Technology
A graph is pancyclic if it contains all cycles from lengths 4 to |V(G)|. An n-dimensional crossed cube, an important variation of hypercube denoted as CQn, has been proved to be pancyclic because it contains all cycles whose lengths range from 4 to |V(CQn|. Since vertex and edge faults may occur when a network is used, it is practical and meaningful to evaluate the performance of a faulty network. Moreover, the vertex fault-tolerant Hamiltonicity and the edge fault-tolerant hamiltonicity measure the performances of the Hamiltonian properties in the faulty networks. From this fault-tolerant concept, we propose using the fault-tolerant pancyclicity of networks to measure the performance of faulty networks. In this paper, we consider a faulty crossed n-cube with vertex and/or edge faults here. Let the faulty set F be a subset of V(CQn) ∪ E(CQn). We prove that any cycle of length l (4 \le l \le |V(CQn| - fv) can be embedded into a faulty crossed n-cube CQn - F with dilation 1, where |F| = fv + fe is less than n -2, fv is the number of faulty vertices of F, fe is the number of faulty edges of F, and n is greater than 2. The results can readily be used in the optimum embedding of a ring of the specified length in a faulty crossed cube.
Citation:
Wen-Tzeng Huang, Woei-kae Chen, Chin-Hsing Chen, "On the Fault-Tolerant Pancyclicity of Crossed Cubes," icpads, pp.483, Ninth International Conference on Parallel and Distributed Systems (ICPADS'02), 2002
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