n-dimensional folded hypercube, denoted by FQn, is an enhanced n-dimensional hypercube with one extra link between nodes that have the furthest Hamming distance. Let FFv (respectively, FFe) denote the set of faulty nodes (respectively, faulty links) in FQn. Under the assumption that every fault-free node in FQn is incident to at least two fault-free links, Hsieh et al. (Inform. Process. Lett. 110 (2009) pp.41-53) showed that if |FFv|+|FFe| ≤ 2n-4 for n ≥ 3, then FQn-FFv-FFe contains a fault-free cycle of length at least 2n-2|FFv|. In this paper, we show that, under the same conditional fault model, FQn with n ≥ 5 can tolerate more faulty elements and provides the same lower bound of the length of a longest fault-free cycle, i.e., FQn-FFv-FFe contains a fault-free cycle of length at least 2n-2|FFv| if |FFv|+|FFe| ≤ 2n-3 for n ≥ 5." />
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Longest Fault-Free Cycles in Folded Hypercubes with Conditional Faulty Elements

Wen-Yin HUANG
Jia-Jie LIU
Jou-Ming CHANG
Ro-Yu WU

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences   Vol.E97-A    No.6    pp.1187-1191
Publication Date: 2014/06/01
Online ISSN: 1745-1337
DOI: 10.1587/transfun.E97.A.1187
Type of Manuscript: Special Section PAPER (Special Section on Discrete Mathematics and Its Applications)
Category: 
Keyword: 
interconnection networks,  hypercubes,  folded hypercubes,  fault-free cycles,  conditional fault model,  

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Summary: 
An n-dimensional folded hypercube, denoted by FQn, is an enhanced n-dimensional hypercube with one extra link between nodes that have the furthest Hamming distance. Let FFv (respectively, FFe) denote the set of faulty nodes (respectively, faulty links) in FQn. Under the assumption that every fault-free node in FQn is incident to at least two fault-free links, Hsieh et al. (Inform. Process. Lett. 110 (2009) pp.41-53) showed that if |FFv|+|FFe| ≤ 2n-4 for n ≥ 3, then FQn-FFv-FFe contains a fault-free cycle of length at least 2n-2|FFv|. In this paper, we show that, under the same conditional fault model, FQn with n ≥ 5 can tolerate more faulty elements and provides the same lower bound of the length of a longest fault-free cycle, i.e., FQn-FFv-FFe contains a fault-free cycle of length at least 2n-2|FFv| if |FFv|+|FFe| ≤ 2n-3 for n ≥ 5.

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