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Original Articles

Linearly many faults in augmented cubes

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Pages 475-483 | Received 19 Apr 2012, Accepted 26 Sep 2012, Published online: 08 Nov 2012

References

  • A. Angjeli, E. Cheng, and L. Lipták, Structural properties of augmented cubes, Technical Report, Series 2012-1, Oakland University, 2012
  • A. Angjeli, Strong connectivity properties of generalizations of the hypercube, Ph.D. thesis, Oakland University (in preparation)
  • Bauer , D. , Boesch , F. , Suffel , C. and Tindell , R. 1981 . “ Connectivity extremal problems and the design of reliable probabilistic networks ” . In The theory and application of graphs , Edited by: Alavi , Y. and Chartrand , G. 89 – 98 . New York : Wiley .
  • Chang , N.-W. and Hsieh , S.-Y. 2012 . Conditional diagnosability of augmented cubes under the PMC model . IEEE Transactions on Dependable and Secure Computing , 9 : 46 – 60 .
  • Chen , Y.-C. and Tan , J.J.M. 2007 . Restricted connectivity for three families of interconnection networks . Applied Mathematics and Computation , 188 : 4877 – 4882 .
  • Chen , Y.-C. , Tan , J.J.M. , Hsu , L.-H. and Kao , S.-S. 2003 . Super-connectivity and super-edge-connectivity for some interconnection networks . Applied Mathematics and Computation , 140 : 245 – 254 .
  • Cheng , E. , Jia , R. and Lu , D. 2010 . Matching preclusion and conditional matching preclusion for augmented cubes . Journal of Interconnection Networks , 11 : 35 – 60 .
  • Cheng , E. , Lipman , M.J. and Lipták , L. 2012 . Matching preclusion and conditional matching preclusion for regular interconnection networks . Discrete Applied Mathematics , 160 : 1936 – 1954 .
  • Cheng , E. and Lipták , L. 2007 . Fault resiliency of Cayley graphs generated by transpositions . International Journal of Foundations of Computer Science , 18 : 1005 – 1022 .
  • Cheng , E. and Lipták , L. 2009 . A kind of conditional vertex connectivity of Cayley graphs generated by transposition trees . Congressus Numerantium , 199 : 167 – 173 .
  • Cheng , E. and Lipták , L. 2007 . Linearly many faults in Cayley graphs generated by transposition trees . Information Sciences , 177 : 4877 – 4882 .
  • Cheng , E. , Lipták , L. , Qiu , K. and Shen , Z. Cyclic vertex-connectivity of cayley graphs generated by transposition trees . Graphs and Combinatorics , DOI: 10.1007/s00373-012-1172-0
  • Cheng , E. , Lipták , L. and Sala , F. 2010 . Linearly many faults in 2-tree-generated networks . Networks , 55 : 90 – 98 .
  • Cheng , E. , Lipman , M.J. and Park , A. 2001 . Super connectivity of star graphs, alternating group graphs, and split-stars . Ars Combinatoria , 59 : 107 – 116 .
  • Choudum , S.A. and Sunitha , V. 2002 . Augmented cubes . Networks , 40 : 71 – 84 .
  • Hellwig , A. , Rautenbach , D. and Volkmann , L. 2005 . Cuts leaving components of given minimum order . Discrete Mathematics , 292 : 55 – 65 .
  • Hong , W.-S. and Hsieh , S.-Y. 2012 . Strong diagnosability and conditional diagnosability of augmented cubes under the comparison diagnosis model . IEEE Transactions on Reliability , 61 : 140 – 148 .
  • Hsieh , S.-Y. and Cian , Y.-R. 2010 . Conditional edge-fault hamiltonicity of augmented cubes . Information Sciences , 180 : 2596 – 2617 .
  • Hsieh , S.-Y. and Shiu , J.-Y. 2007 . Cycle embedding of augmented cubes . Applied Mathematics and Computation , 191 : 314 – 319 .
  • Ma , M. , Liu , G. and Xu , J.-M. 2008 . The super connectivity of augmented cubes . Information Processing Letters , 106 : 59 – 63 .
  • Plummer , M. 1972 . “ On the cyclic connectivity of planar graphs ” . In Graph Theory and Applications: Lecture Notes in Mathematics , 235 – 242 . Berlin/Heidelberg : Springer .
  • Qi , Z.B. , Ye , D. and Zhang , H.P. 2009 . The relation between cyclic edge-connectivity and cyclic connectivity of 3-regular connected graphs . Journal of Shandong University (Natural Science) , 12 : 22 – 24 .
  • Wan , M. and Zhang , Z. 2009 . A kind of conditional vertex connectivity of star graphs . Applied Mathematics Letters , 22 : 264 – 267 .
  • Yang , X. , Evans , D.J. , Chen , B. , Megson , G.M. and Lai , H. 2004 . On the maximal connected component of hypercube with faulty vertices . International Journal of Computer Mathematics , 81 : 515 – 525 .
  • Yang , X. , Evans , D.J. and Megson , G.M. 2004 . On the maximal connected component of hypercube with faulty vertices II . International Journal of Computer Mathematics , 81 : 1175 – 1185 .
  • Yang , X. , Evans , D.J. and Megson , G.M. 2006 . On the maximal connected component of hypercube with faulty vertices III . International Journal of Computer Mathematics , 83 : 27 – 37 .
  • Zhang , Z. , Xiong , W. and Yang , W. 2010 . A kind of conditional fault tolerance of alternating group graphs . Information Processing Letters , 110 ( 22 ) : 998 – 1002 .

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