Title: Edge-bipancyclicity of conditional faulty hypercubes
Authors: Shih, Lun-Min
Tan, Jimmy J. M.
Hsu, Lih-Hsing
Department of Computer Science
Keywords: cycles;pancyclic;conditional fault;hypercube;fault-tolerant;interconnection networks
Issue Date: 31-Dec-2007
Abstract: Xu et al. showed that for any set of faulty edges F of an n-dimensional hypercube Q(n) with vertical bar F vertical bar <= n - 1, each edge of Q(n) - F lies on a cycle of every even length from 6 to 2(n), n >= 4, provided not all edges in F are incident with the same vertex. In this paper, we find that under similar condition, the number of faulty edges can be much greater and the same result still holds. More precisely, we show that, for up to vertical bar F vertical bar = 2n - 5 faulty edges, each edge of the faulty hypercube Q(n) - F lies on a cycle of every even length from 6 to 2(n) with each vertex having at least two healthy edges adjacent to it, for n >= 3. Moreover, this result is optimal in the sense that there is a set F of 2n - 4 conditional faulty edges in Q(n) such that Q(n) - F contains no hamiltonian cycle. (c) 2007 Elsevier B.V. All rights reserved.
URI: http://dx.doi.org/10.1016/j.ipl.2007.07.009
ISSN: 0020-0190
DOI: 10.1016/j.ipl.2007.07.009
Volume: 105
Issue: 1
Begin Page: 20
End Page: 25
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