Vertex-pancyclicity of twisted cubes with maximal faulty edges

References

• Abraham , S. and Padmanabhan , K. 1991 . The twisted cube topology for multiprocessors: A study in network asymmetry . J. Parallel Distrib. Comput. , 13 : 104 – 110 .
   Web of Science ®Google Scholar
• Ascheuer , N. Hamiltonian path problems in the on-line optimization of flexible manufacturingsystems PhD thesis, University of Technology, Berlin, Germany, 1995. Available at ftp://ftp.zib.de/pub/zib-publications/reports/TR-96-03.ps
   Google Scholar
• Chang , C. P. , Wang , J. N. and Hsu , L. H. 1999 . Topological properties of twisted cubes . Inf. Sci. , 113 : 147 – 167 .
   Web of Science ®Google Scholar
• Chang , J. M. and Yang , J. S. 2008 . Fault-tolerant cycle-embedding in alternating group graphs . Appl. Math. Comput. , 197 : 760 – 767 .
   Web of Science ®Google Scholar
• Chang , J. M. , Yang , J. S. , Wang , Y. L. and Cheng , Y. 2004 . Panconnectivity, fault- tolerant Hamiltonicity and Hamiltonian-connectivity in alternating group graphs . Networks , 44 ( 4 ) : 302 – 310 .
   Web of Science ®Google Scholar
• Fan , J. , Jia , X. and Lin , X. 2007 . Optimal embeddings of paths with various length in twisted cubes . IEEE Trans. Parallel Distrib. Syst. , 18 ( 4 ) : 511 – 521 .
   Web of Science ®Google Scholar
• Fan , J. , Jia , X. and Lin , X. 2008 . Embedding of cycles in twisted cubes with edge-pancyclic . Algorithmica , 51 ( 3 ) : 264 – 282 .
   Web of Science ®Google Scholar
• Fan , J. , Lin , X. and Jia , X. 2004 . Node-pancyclicity and edge-pancyclicity of crossed cubes . Inf. Process. Lett. , 93 : 133 – 138 .
   Web of Science ®Google Scholar
• Fan , J. , Lin , X. , Jia , X. and Lau , R. W.H. Edge-pancyclicity of twisted cubes . Proceedings of the 16th Annual International Symposium on Algorithms and Computation (ISAAC) . Sanya, Hainan , China. Vol. 3827 , pp. 1090 – 1099 . Lecture Notes in Computer Science
   Google Scholar
• Fu , J. S. Conditional fault-tolerant Hamiltonicity of twisted cubes . Proceedings of the 7th International Conference on Parallel and Distributed Computing, Applications and Technologies (PDCAT) . Taipei , Taiwan. pp. 5 – 10 .
   Google Scholar
• Fu , J. S. 2008 . Fault-free Hamiltonian cycles in twisted cubes with conditional link faults . Theor. Comput. Sci. , 407 ( 1–3 ) : 318 – 329 .
   Web of Science ®Google Scholar
• Fu , J. S. 2010 . Edge-fault-tolerant vertex-pancyclicity of augmented cubes . Inf. Process. Lett. , 110 : 439 – 443 .
   Web of Science ®Google Scholar
• Hsieh , S. Y. and Chang , N. W. 2006 . Hamiltonian path embedding and pancyclicity on the Möbius cube with both faulty nodes and faulty edges . IEEE Trans. Comput. , 55 ( 7 ) : 854 – 863 .
   Web of Science ®Google Scholar
• Hsieh , S. Y. and Lee , C. W. 2009 . Conditional edge-fault hamiltonicity of matching composition networks . IEEE Trans. Parallel Distrib. Syst , 20 ( 4 ) : 581 – 592 .
   Web of Science ®Google Scholar
• Hsieh , S. Y. and Lee , C. W. 2010 . Pancyclicity of restricted hypercube-like networks under the conditional fault model . SIAM J. Discrete Math , 23 ( 4 ) : 2010 – 2019 .
   Web of Science ®Google Scholar
• Hibers , P. A.J. , Koopman , M. R.J. and van de Snepscheut , J. L.A. The twisted cube . Proceedings of the Conference on Parallel Architectures and Languages Europe . Eindhoven , The Netherlands. pp. 152 – 159 . Lecture Notes in Computer Science, Springer
   Google Scholar
• Huang , W. T. , Tan , J. M. , Hung , C. N. and Hsu , L. H. 2002 . Fault-tolerant Hamiltonianicity of twisted cubes . J. Parallel Distrib. Comput. , 62 : 591 – 604 .
   Web of Science ®Google Scholar
• Lai , P. L. and Hsu , H. C. 2008 . The two-equal-disjoint path cover problem of matching composition network . Inf. Process. Lett. , 107 ( 1 ) : 18 – 23 .
   Web of Science ®Google Scholar
• Lai , C. J. and Tsai , C. H. 2008 . Embedding a family of meshes into twisted cubes . Inf. Process. Lett , 108 ( 5 ) : 326 – 330 .
   Web of Science ®Google Scholar
• Leighton , F. T. 1992 . Introduction to Parallel Algorithms and Architecture: Arrays· Trees· Hypercubes , San Francisco , CA : Morgan Kaufmann .
   Google Scholar
• Li , T. K. , Yang , M. C. , Tan , J. M. and Hsu , L. H. 2006 . On embedding cycle in faulty twisted cubes . Inf. Sci. , 176 : 676 – 690 .
   Web of Science ®Google Scholar
• Ma , M. , Liu , G. and Xu , J. M. 2007 . Panconnectivity and edge-fault-tolerant pancyclicity of augmented cubes . Parallel Comput. , 33 : 36 – 42 .
   Web of Science ®Google Scholar
• Park , J. H. 2008 . Panconnectivity and edge-pancyclicity of faulty recursive circulant G(2m, 4) . Theor. Comput. Sci. , 390 : 70 – 80 .
   Web of Science ®Google Scholar
• Park , J.-H. , Lim , H.-S. and Kim , H.-C. 2007 . Panconnectivity and pancyclicity of hypercube-like interconnection networks with faulty elements . Theor. Comput. Sci. , 377 : 170 – 180 .
   Web of Science ®Google Scholar
• Saad , Y. and Schultz , M. H. 1988 . Topological properties of hypercubes . IEEE Trans. Comput , 37 ( 7 ) : 867 – 872 .
   Web of Science ®Google Scholar
• Xu , M. and Xu , J. M. 2005 . Edge-pancyclicity of Mobius cubes . Inf. Process. Lett , 96 ( 4 ) : 136 – 140 .
   Web of Science ®Google Scholar
• West , D. B. 2001 . Introduction to Graph Theory , 2 , Upper Saddle River , NJ : Prentice Hall .
   Google Scholar