Conditional fault-tolerant routing of (n, k)-star graphs

References

• J. Al-Sadi, K. Day, and M. Ould-Khaoua, A new fault-tolerant routing algorithm for k-ary n-cube networks, Int. J. High Speed Comput. 12(1) (2004), pp. 29–54. doi: 10.1142/S0129053304000220
   Google Scholar
• C.-P. Chang and C.-C. Wu, Conditional fault diameter of crossed cubes, J. Parallel Distrib. Comput. 69 (2009), pp. 91–99. doi: 10.1016/j.jpdc.2008.08.001
   Web of Science ®Google Scholar
• N.-W. Chang, W.-H. Deng, and S.-Y. Hsieh, Conditional diagnosability of (n,k)-star networks under the comparison diagnosis model, IEEE Trans. Reliab. 64(1) (2015), pp. 132–143. doi: 10.1109/TR.2014.2354912
   Web of Science ®Google Scholar
• E. Cheng and M.J. Lipman, On fault-tolerant routing in (n,k)-star graphs, Congr. Numer. 155 (2002), pp. 25–31.
   Google Scholar
• E. Cheng, J.W. Grossman, L. Lipták, K. Qiu, and Z. Shen, Distance formula and shortest paths for the (n,k)-star graphs, Inf. Sci. 180 (2010), pp. 1671–1680. doi: 10.1016/j.ins.2010.01.016
   Web of Science ®Google Scholar
• E. Cheng, K. Qiu, and Z. Shen, The number of shortest paths in the (n,k)-star graphs, Discrete Math. Algorithms Appl. 6(4) (2014), pp. 1793–8309. doi: 10.1142/S1793830914500517
   Google Scholar
• W.-K. Chiang and R.-J. Chen, The (n,k)-star graph: A generalized star graph, Inform. Process. Lett. 56(5) (1995), pp. 259–264. doi: 10.1016/0020-0190(95)00162-1
   Web of Science ®Google Scholar
• W.-K. Chiang and R.-J. Chen, Topological properties of the (n,k)-star graph, Int. J. Found. Comput. Sci. 9(2) (1998), pp. 235–248. doi: 10.1142/S0129054198000167
   Google Scholar
• K. Day, The conditional node connectivity of the k-ary n-cube, J. Interconnection Networks 5(1) (2004), pp. 13–26. doi: 10.1142/S0219265904001003
   Google Scholar
• D.-R. Duh, T.-L. Chen, and Y.-L. Wang, (n−3)-edge-fault-tolerant weak-pancyclicity of (n,k)-star graphs, Theoret. Comput. Sci. 516 (2014), pp. 28–39. doi: 10.1016/j.tcs.2013.11.013
   Web of Science ®Google Scholar
• A.H. Esfahanian, Generalized measures of fault tolerance with application to N-cube networks, IEEE Trans. Comput. 38(11) (1989), pp. 1586–1591. doi: 10.1109/12.42131
   Web of Science ®Google Scholar
• J. Fan, S. Zhang, X. Jia, and G. Zhang, A Fault-free Unicast Algorithm in Twisted Cubes with the Restricted Faulty Node Set, 15th International Conference on Parallel and Distributed Systems (ICPADS), Shenzhen, 2009, pp. 316–323.
   Google Scholar
• Q.-P. Gu and S. Peng, Node-to-node cluster fault tolerant routing in star graphs, Inform. Process. Lett. 56 (1995), pp. 29–35. doi: 10.1016/0020-0190(95)00135-Y
   Web of Science ®Google Scholar
• Q.-P. Gu and S. Peng, Node-to-set disjoint paths problem in star graphs, Inform. Process. Lett. 62 (1997), pp. 201–207. doi: 10.1016/S0020-0190(97)00059-8
   Web of Science ®Google Scholar
• Q.-P. Gu and S. Peng, Cluster fault-tolerant routing in star graphs, Networks 35(1) (2000), pp. 83–90. doi: 10.1002/(SICI)1097-0037(200001)35:1<83::AID-NET7>3.0.CO;2-D
   Web of Science ®Google Scholar
• F. Harary, Graph Theory, Addison-Wesley, Reading, MA, 1969.
   Google Scholar
• L.-H. Hsu, H.-M. Hung, H.-C. Hsu, and C.-K. Lin, The spanning connectivity of the (n,k)-star graphs, Internat. J. Found. Comput. Sci. 17(2) (2006), pp. 415–434. doi: 10.1142/S0129054106003905
   Web of Science ®Google Scholar
• S. Latifi, M. Hegde, and M. Naraghi-Pour, Conditional connectivity measures for large multiprocessor systems, IEEE Trans. Comput. 43(2) (1994), pp. 218–222. doi: 10.1109/12.262126
   Web of Science ®Google Scholar
• T.-C. Lin and D.-R. Duh, Constructing vertex-disjoint paths in (n,k)-star graphs, Inform. Sci. 178(3) (2008), pp. 788–801. doi: 10.1016/j.ins.2007.09.014
   Web of Science ®Google Scholar
• T.-C. Lin, D.-R. Duh, and H.-C. Cheng, Wide Diameters of (n,k)-Star Networks, Proceedings of the International Conference on Computing, Communications, and Control Technologies (CCCT04), Austin, Texas, 2004, pp. 160–165.
   Google Scholar
• Y. Lv and X. Ruan, The Conditional Fault Tolerance of (n,2)-Star Graph, 2nd International Conference on Information Science and Engineering (ICISE), 2010, pp. 4767–4769.
   Google Scholar
• Y. Lv and Y. Xiang, The conditional connectivity of (n,k)-star graph, Periodical: Adv. Mater. Res.: Main Theme Materials Science and Information Technology 433–440 (2012), pp. 4853–4856.
   Google Scholar
• Y. Rouskov, S. Latifi, and P.K. Srimani, Conditional fault diameter of star graph networks, J. Parallel Distrib. Comput. 33(1) (1996), pp. 91–97. doi: 10.1006/jpdc.1996.0028
   Web of Science ®Google Scholar
• Y. Xiang and I.A. Stewart, One-to-many node-disjoint paths in (n,k)-star graphs, Discrete Appl. Math. 158(1) (2010), pp. 62–70. doi: 10.1016/j.dam.2009.08.013
   Web of Science ®Google Scholar
• D. Xiang, A. Chen, and J. Sun, Fault-tolerant routing and multi-casting in hypercubes using a partial path set-up, Parallel Comput. 31(3–4) (2005), pp. 389–411. doi: 10.1016/j.parco.2005.03.001
   Web of Science ®Google Scholar
• A. Yuan, E. Cheng, and L. Lipták, Linearly many faults in (n,k)-star graphs, Int. J. Found. Comput. Sci. 22(7) (2011), pp. 1729–1745. doi: 10.1142/S0129054111008994
   Web of Science ®Google Scholar