Unchanging the diameter of k-ary n-cube networks with faulty vertices

References

• N.R. Adiga, M.A. Blumrich, D. Chen, P. Coteus, A. Gara, M.E. Giampapa, P. Heidelberger, S. Singh, B.D. Steinmacher-Burow, T. Takken, M. Tsao, and P. Vranas, Blue Gene/L torus interconnection network, IBM J. Res. Dev. 49(2) (2005), pp. 265–276. doi: 10.1147/rd.492.0265
   Web of Science ®Google Scholar
• Y.A. Ashir and I.A. Stewart, On embedding cycles in k-ary n-cubes, Parallel Process. Lett. 7 (1997), pp. 49–55. doi: 10.1142/S0129626497000073
   Google Scholar
• W.C. Athas and C.L. Seitz, Multicomputers: message-passing concurrent computers, Computer 21 (1988), pp. 9–24. doi: 10.1109/2.73
   Web of Science ®Google Scholar
• I. Banič and J. Žerovnik, Fault-diameter of Cartesian graph bundles, Inform. Process. Lett. 100 (2006), pp. 47–51. doi: 10.1016/j.ipl.2006.05.010
   Web of Science ®Google Scholar
• I. Banič and J. Žerovnik, The fault-diameter of Cartesian products, Adv. Appl. Math. 40 (2008), pp. 98–106. doi: 10.1016/j.aam.2007.04.005
   Web of Science ®Google Scholar
• J.A. Bondy and U.S.R. Murty, Graph Theory, Springer, New York, 2007.
   Google Scholar
• B. Bose, B. Broeg, Y. Kwon, and Y. Ashir, Lee distance and topological properties of k-ary n-cubes, IEEE Trans. Comput. 44(8) (1995), pp. 1021–1030. doi: 10.1109/12.403718
   Web of Science ®Google Scholar
• N.-W. Chang, T.-Y. Lin, and S.-Y. Hsieh, Conditional diagnosability of k-ary n-cubes under the PMC model, ACM Trans. Des. Automat. Electron. Syst. 17(4) (2012). Article No. 46. doi: 10.1145/2348839.2348850
   Google Scholar
• K. Day and A. Elah Al-Ayyoub, Fault diameter of k-ary n-cube networks, IEEE Trans. Parallel Distrib. Syst. 8(9) (1997), pp. 903–907. doi: 10.1109/71.615436
   Web of Science ®Google Scholar
• T.H. Dunigan, Performance of the intel iPSC/860 and Ncube 6400 hypercubes, Parallel Comput. 17(10–11) (1991), pp. 1285–1302. doi: 10.1016/S0167-8191(05)80039-0
   Web of Science ®Google Scholar
• N. Graham and F. Harary, Changing and unchanging the diameter of a hypercube, Discrete Appl. Math. (37–38) (1992), pp. 265–274. doi: 10.1016/0166-218X(92)90137-Y
   Web of Science ®Google Scholar
• S.-Y. Hsieh and Y.-H. Chang, Extraconnectivity of k-ary n-cube networks, Theoret. Comput. Sci. 443(20) (2012), pp. 63–69. doi: 10.1016/j.tcs.2012.03.030
   Web of Science ®Google Scholar
• S.-Y. Hsieh and C.-Y. Kao, The conditional diagnosability of k-ary n-cubes under the comparison diagnosis model, IEEE Trans. Comput. 62(4) (2013), pp. 839–843. doi: 10.1109/TC.2012.18
   Web of Science ®Google Scholar
• S.-Y. Hsieh and T.-J. Lin, Panconnectivity and edge-pancyclicity of k-ary n-cubes, Networks 54(1) (2009), pp. 1–11. doi: 10.1002/net.20290
   Web of Science ®Google Scholar
• R.E. Kessler and J.L. Schwarzmeier, Cray T3D: A New Dimension for Cray Research, Proceedings of 38th IEEE Computer Society International Conference, IEEE Press, 1993, pp. 176–182.
   Google Scholar
• M.S. Krishnamoorthy and B. Krishnamurthy, Fault diameter of interconnection networks, Comput. Math. Appl. 13(5) (1987), pp. 577–582. doi: 10.1016/0898-1221(87)90085-X
   Web of Science ®Google Scholar
• F.T. Leighton, Introduction to Parallel Algorithms and Architectures: Arrays, Trees, Hypercubes, Morgan Kaufmann, San Francisco, 1992.
   Google Scholar
• W. Mao and D.M. Nicol, On k-ary n-cubes: theory and applications, Discrete Appl. Math. 129(1) (2003), pp. 171–193.
   Google Scholar
• C. Peterson, J. Sutton, and P. Wiley, iWarp: A 100-MOPS LIW microprocessor for multicomputers, IEEE Micro 11(2) (1991), pp. 26–37. doi: 10.1109/40.87568
   Web of Science ®Google Scholar
• J.-J. Wang, T.-Y. Ho, D. Ferrero, and T.-Y. Sung, Diameter variability of cycles and tori, Inform. Sci. 178(14) (2008), pp. 2960–2967. doi: 10.1016/j.ins.2008.03.008
   Web of Science ®Google Scholar
• S. Wang, J. Li, and R. Wang, Hamiltonian paths and cycles with prescribed edges in the 3-ary n-cube, Inform. Sci. 181(14) (2011), pp. 3054–3065. doi: 10.1016/j.ins.2011.03.011
   Web of Science ®Google Scholar
• S. Wang, Y. Yang, J. Li, and S. Lin, Hamiltonian cycles passing through linear forests in k-ary n-cubes, Discrete Appl. Math. 159(14) (2011), pp. 1425–1435. doi: 10.1016/j.dam.2011.05.008
   Web of Science ®Google Scholar
• M. Xu, J.-M. Xu, and X.-M. Hou, Fault diameter of Cartesian product graphs, Inform. Process. Lett. 93 (2005), pp. 245–248. doi: 10.1016/j.ipl.2004.11.005
   Web of Science ®Google Scholar