research-article

Fault-Tolerant Hamiltonicity of Twisted Cubes

Authors:

Wen-Tzeng Huang,

Jimmy J.M. Tan,

Chun-Nan Hung,

Lih-Hsing HsuAuthors Info & Claims

Journal of Parallel and Distributed Computing, Volume 62, Issue 4

Pages 591 - 604

https://doi.org/10.1006/jpdc.2001.1813

Published: 01 April 2002 Publication History

Abstract

The twisted cube TQn, is derived by changing some connection of hypercube Qn according to specific rules. Recently, many topological properties of this variation cube are studied. In this paper, we consider a faulty twisted n-cube with both edge and/or node faults. Let F be a subset of V(TQn) E(TQn), we prove that TQn F remains hamiltonian if |F| n 2. Moreover, we prove that there exists a hamiltonian path in TQn F joining any two vertices u, v in V(TQn) F if |F| n 3. The result is optimum in the sense that the fault-tolerant hamiltonicity (fault-tolerant hamiltonian connectivity respectively) of TQn is at most n 2 (n 3 respectively).

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Cited By

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Hung RLi CChen JSu Q(2017)The Hamiltonian connectivity of rectangular supergrid graphsDiscrete Optimization10.1016/j.disopt.2017.06.00126:C(41-65)Online publication date: 1-Nov-2017
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Zhu X(2017)A Hypercube Variant with Small DiameterJournal of Graph Theory10.1002/jgt.2209685:3(651-660)Online publication date: 1-Jul-2017
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Index Terms

Fault-Tolerant Hamiltonicity of Twisted Cubes

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Reviews

Reviewer: Ory B Kushnir

The authors prove an interesting and important graph theoretic property of twisted cubes. Such cubes, popular in fault tolerant network design, are shown to be tolerant of up to n-3 faults. They are also shown to remain Hamiltonian for up to n-2 faults. Following a brief introduction to their conventions, the authors construct the twisted cube using the usual recursive construction on top of TQ1 . TQ3 is shown to illustrate how the nth dimensional cube might look, and is later used in intermediate lemmas. The overall proof is, as might be expected, by way of induction. The audience for this publication would most likely be mathematicians and engineers working on parallel processing on multiple central processing unit (CPU) networks. To a lesser extent, engineers working on complex wide area networks (WANs) may also find this an interesting read. The reference list is concise and highly relevant. Online Computing Reviews Service

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cover image Journal of Parallel and Distributed Computing

Journal of Parallel and Distributed Computing Volume 62, Issue 4

April 2002

247 pages

ISSN:0743-7315

Issue’s Table of Contents

Publisher

Academic Press, Inc.

United States

Publication History

Published: 01 April 2002

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Hung RLi CChen JSu Q(2017)The Hamiltonian connectivity of rectangular supergrid graphsDiscrete Optimization10.1016/j.disopt.2017.06.00126:C(41-65)Online publication date: 1-Nov-2017
https://dl.acm.org/doi/10.1016/j.disopt.2017.06.001
Liu YLiu W(2017)Fractional matching preclusion of graphsJournal of Combinatorial Optimization10.1007/s10878-016-0077-x34:2(522-533)Online publication date: 1-Aug-2017
https://dl.acm.org/doi/10.1007/s10878-016-0077-x
Zhu X(2017)A Hypercube Variant with Small DiameterJournal of Graph Theory10.1002/jgt.2209685:3(651-660)Online publication date: 1-Jul-2017
https://dl.acm.org/doi/10.1002/jgt.22096
(2015)The property of edge-disjoint Hamiltonian cycles in transposition networks and hypercube-like networksDiscrete Applied Mathematics10.1016/j.dam.2014.09.006181:C(109-122)Online publication date: 30-Jan-2015
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Hung R(2013)DVcubeTheoretical Computer Science10.1016/j.tcs.2013.06.001498(28-45)Online publication date: 1-Aug-2013
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Cheng EKe QShen Z(2011)On the surface area of the asymmetric twisted cubeProceedings of the 5th international conference on Combinatorial optimization and applications10.5555/2032927.2032959(411-423)Online publication date: 4-Aug-2011
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Hung R(2011)Embedding two edge-disjoint Hamiltonian cycles into locally twisted cubesTheoretical Computer Science10.1016/j.tcs.2011.05.004412:35(4747-4753)Online publication date: 1-Aug-2011
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Fan JJia XCheng BYu J(2011)An efficient fault-tolerant routing algorithm in bijective connection networks with restricted faulty edgesTheoretical Computer Science10.1016/j.tcs.2011.02.014412:29(3440-3450)Online publication date: 1-Jul-2011
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Lai P(2011)Geodesic pancyclicity of twisted cubesInformation Sciences: an International Journal10.1016/j.ins.2011.07.030181:23(5321-5332)Online publication date: 1-Dec-2011
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Fan JJia XLiu XZhang SYu J(2011)Efficient unicast in bijective connection networks with the restricted faulty node setInformation Sciences: an International Journal10.1016/j.ins.2010.12.011181:11(2303-2315)Online publication date: 1-Jun-2011
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Abstract

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Edge-fault-tolerant node-pancyclicity of twisted cubes

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