Edge-fault-tolerant bipancyclicity of Cayley graphs generated by transposition-generating trees

References

• S. Akers and B. Krishnamurthy, A group-theoretic model for symmetric interconnection networks, IEEE Trans. Comput. 38 (1989), pp. 555–565. doi: 10.1109/12.21148
   Web of Science ®Google Scholar
• T. Araki, Hyper hamiltonian laceability of Cayley graphs generated by transpositions, Networks 48 (2006), pp. 121–124. doi: 10.1002/net.20126
   Web of Science ®Google Scholar
• T. Araki and Y. Kikuchi, Hamiltonian laceability of bubble-sort graphs with edge faults, Inform. Sci. 177 (2007), pp. 2679–2691. doi: 10.1016/j.ins.2007.01.017
   Web of Science ®Google Scholar
• E. Cheng and L. Lipták, Linearly many faults in Cayley graphs generated by transposition trees, Inform. Sci. 177 (2007), pp. 4877–4882. doi: 10.1016/j.ins.2007.05.034
   Web of Science ®Google Scholar
• E. Cheng and L. Lipták, Diagnosability of Cayley graphs generated by transposition trees with missing edges, Inform. Sci. 238 (2013), pp. 250–252. doi: 10.1016/j.ins.2013.03.009
   Web of Science ®Google Scholar
• E. Cheng, L. Lipták, and K. Qiu, Cyclic vertex-connectivity of Cayley graphs generated by transposition trees, Graphs Combin. 29 (2013), pp. 835–841. doi: 10.1007/s00373-012-1172-0
   Web of Science ®Google Scholar
• J. Fu, Conditional fault-tolerant hamiltonicity of star graphs, Parallel Comput. 33 (2007), pp. 488–496. doi: 10.1016/j.parco.2007.02.007
   Web of Science ®Google Scholar
• C. Godsil and G. Royle, Algebraic Graph Theory, Springer, New York, 2004.
   Google Scholar
• S. Hsieh, G. Chen, and C. Ho, Hamiltonian-laceability of star graphs, Networks 36 (2000), pp. 225–232. doi: 10.1002/1097-0037(200012)36:4<225::AID-NET3>3.0.CO;2-G
   Web of Science ®Google Scholar
• S.Y. Hsieh and C.H. Chen, Pancyclicity on Möbius cubes with maximal edge faults, Parallel Comput. 30 (2004), pp. 407–421. doi: 10.1016/j.parco.2003.12.003
   Web of Science ®Google Scholar
• W.T. Huang, W.k. Chen, and C.H. Chen, On the fault-tolerant pancyclicity of crossed cubes, Proceedings of the 9th International Conference on Parallel and Distributed Systems, Taiwan, ROC, 2002, pp. 483–488.
   Google Scholar
• H.S. Hung, J.S. Fu, and G.H. Chen, Fault-free Hamiltonian cycles in crossed cubes with conditional link faults, Inform. Sci. 177 (2007), pp. 5664–5674. doi: 10.1016/j.ins.2007.05.032
   Web of Science ®Google Scholar
• J.-S. Jwo, S. Lakshmivarahan, and S.K. Dhall, Embedding of cycles and grids in star graphs, J. Circuits, Syst. Comput. 1 (1991), pp. 43–74. doi: 10.1142/S0218126691000215
   Google Scholar
• Y. Kikuchi and T. Araki, Edge-bipancyclicity and edge-fault-tolerant bipancyclicity of bubble-sort graphs, Inform. Process. Lett. 100 (2006), pp. 52–59. doi: 10.1016/j.ipl.2006.05.012
   Web of Science ®Google Scholar
• V. Kompel′makher and V. Liskovets, Sequential generation of arrangements by means of a basis of transpositions, Kibernetica 3 (1975), pp. 17–21.
   Google Scholar
• S. Lakshmivarahan, J.-S. Jwo, and S. Dhall, Symmetry in interconnection networks based on Cayley graphs of permutation groups: A survey, Parallel Comput. 19 (1993), pp. 361–407. doi: 10.1016/0167-8191(93)90054-O
   Web of Science ®Google Scholar
• T. Li, J.J. Tan and L. Hsu, Hyper hamiltonian laceablity on edge fault star graph, Inform. Sci. 165 (2004), pp. 59–71. doi: 10.1016/j.ins.2003.09.023
   Web of Science ®Google Scholar
• H. Li, W. Yang and J. Meng, Fault-tolerant Hamiltonian laceability of Cayley graphs generated by transposition trees, Discret. Math. 312 (2012), pp. 3087–3095. doi: 10.1016/j.disc.2012.06.007
   Web of Science ®Google Scholar
• Y. Tanaka, Y. Kikuchi, T. Araki, and Y. Shibata, Bipancyclic properties of Cayley graphs generated by transpositions, Discret. Math. 310 (2010), pp. 748–754. doi: 10.1016/j.disc.2009.09.002
   Web of Science ®Google Scholar
• M. Tchuente, Generation of permutations by graphical exchanges, ARS Combinatria 14 (1982), pp. 115–122.
   Google Scholar
• P.Y. Tsai, J.S. Fu, and G.H. Chen, Fault-free longest paths in star networks with conditional link faults, Theoret. Comput. Sci. 410 (2009), pp. 766–775. doi: 10.1016/j.tcs.2008.11.012
   Web of Science ®Google Scholar
• Y.C. Tseng, S.H. Chang, and J.P. Sheu, Fault-tolerant ring embedding in a star graph with both link and node failures, IEEE Trans. Parallel Distrib. Syst. 8 (1997), pp. 1185–1195. doi: 10.1109/71.640010
   Web of Science ®Google Scholar
• M. Xu, X. Hu, and Q. Zhu, Edge-bipancyclicity of star graphs under edge-fault tolerant, Appl. Math. Comput. 183 (2006), pp. 972–979. doi: 10.1016/j.amc.2006.05.117
   Web of Science ®Google Scholar
• W. Yang, H. Li and J. Meng, Conditional connectivity of Cayley graphs by transposition trees, Inform. Process. Lett. 110 (2010), pp. 1027–1030. doi: 10.1016/j.ipl.2010.09.001
   Web of Science ®Google Scholar
• M.C. Yang, T.K. Li, J.J.M. Tan, and L.H. Hsu, Fault-tolerant pancyclicity of the Möbius cubes, IEICE Trans. Fundam. E88-A (2005), pp. 346–352. doi: 10.1093/ietfec/E88-A.1.346
   Web of Science ®Google Scholar
• M. Xu, X. Hu, and Q. Zhu, Edge-bipancyclicity of star graphs under edge-fault tolerant, Appl. Math. Comput. 183 (2006), pp. 972–979. doi: 10.1016/j.amc.2006.05.117
   Web of Science ®Google Scholar