DMCA
Fault-free Paths in Hypercubes with More Faulty Nodes (2008)
| Venue: | PROC. OF THE 19TH WORKSHOP ON COMBINATORIAL MATHEMATICS AND COMPUTATION THEORY |
BibTeX
@MISC{Kueng08fault-freepaths,
author = {Tz-liang Kueng and Tyne Liang and Jimmy J. M. Tan and Lih-hsing Hsu},
title = { Fault-free Paths in Hypercubes with More Faulty Nodes},
year = {2008}
}
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Abstract
Faults in a network may take various forms such as hardware/software errors, node/link faults, etc. In this paper, node-faults are addressed. Let F be a faulty set of f ≤ 2n − 6 conditional node-faults in an injured n-cube Qn such that every node of Qn still has at least two fault-free neighbors. Then we show that Qn−F contains a path of length at least 2 n − 2f − 1 (respectively, 2 n − 2f − 2) between any two nodes of odd (respectively, even) distance. Since an n-cube is a bipartite graph, such kind of the fault-free path turns out to be the longest one in the case when all faulty nodes belong to the same partite set.
