Fault-tolerant embedding of paths in crossed cubes

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Abstract

The crossed cube C Qn is an important variant of the hypercube Qn and possesses many desirable properties for interconnection networks. This paper shows that in C Qn with fv faulty vertices and fe faulty edges there exists a fault-free path of length ℓ between any two distinct fault-free vertices for each ℓ satisfying 2n - 1 - 1 ≤ ℓ ≤ 2n - fv - 1 provided that fv + fe ≤ n - 3, where the lower bound of ℓ and the upper bound of fv + fe are tight for some n. Moreover, this result improves the known result that C Qn is (n - 3)-Hamiltonian connected. © 2008 Elsevier B.V. All rights reserved.

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Ma, M., Liu, G., & Xu, J. M. (2008). Fault-tolerant embedding of paths in crossed cubes. Theoretical Computer Science, 407(1–3), 110–116. https://doi.org/10.1016/j.tcs.2008.05.002

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