The Study of Vertices Fault-Tolerance for Edge-Bipancyclicity of Hypercube 林雨淳、洪春男
E-mail: [email protected]
ABSTRACT
This thesis is a discussion of nature about study of vertex fault-tolerance for multiple spanning paths in n-dimensional hypercube. We will further investigate more related vertex fault-tolerant Hamiltonian properties of more bipartite interconnection networks.
Keywords : hypercube ; edge-bipancyclic ; vertices fault-tolerance
Table of Contents
Chapter1 Introduction...1 Chapter2 Preliminaries...4 Chapter3 Vertex fault tolerance for multiple spanning paths in hypercube...6 Chapter4 Vertices fault-tolerance for edge-bipancyclicity of hypercube...28 Chapter5 Conclusion...31 Reference...32
REFERENCES
[1] Toru Araki, Yosuke Kikuchi, “Hamiltonian laceability of bubble-sort graphs with edge faults,” Information Sciences, vol.177, pp.2679-2691 (2007).
[2] Y-Chuang Chen, Chang-Hsiung Tsai, Lih-Hsing Hsu, Jimmy J.M. Tan, “On some super fault-tolerant Hamiltonian graphs,” Applied Mathematics and Computation, vol.148, pp.729-741 (2004).
[3] Rostislav Caha and Vclav Koubek, “Spanning multi-paths in hypercubes,” Discrete Mathematics, Vol. 307, Issue 16, pp.2053-2066 (2007).
[4] Jianxi Fan, Xiaola Lin, Yi Pan, Xiaohua Jia, “Optimal fault-tolerant embedding of paths in twisted cubes,” J. Parallel Distrib. Comput., vol.67, pp.205 - 214 (2007).
[5] J. S. Fu, “Fault-tolerant cycle embedding in the hypercube,” Parallel Computing, 29, pp.821-832, (2003).
[6] J. S. Fu, “Longest fault-free paths in hypercubes with vertex faults,” Information Processing Letters, 176, pp. 759-771, (2006) [7] Tomas Dvorak, Petr Gregor, “Hamiltonian paths with prescribed edges in hypercubes,” Discrete Mathematics, vol.307, pp.1982 - 1998 (2007).
[8] Petr Gregor, Tomas Dvorak, “Path partitions of hypercubes,” Information Processing Letters, vol.108, pp. 402 - 406 (2008).
[9] Ko-Chen Hu, Chun-Nan Hung and Chia-Cheng Chen, “Edge Fault-tolerant Hamiltonian Laceability of Bipartite Hypercube-like Networks,
” Proceedings of the 22nd Workshop on Combinatorial Mathematics and Computational Theory, pp.129-133 (2005).
[10] S. Y. Hsieh, “Fault-tolerant cycle embedding in the hypercube with more both faulty vertices and faulty edges,” Parallel Computing, vol.
32, pp.84-91, (2006).
[11] S. Y. Hsieh, “Embedding longest fault-free paths onto star graphs with more vertex faults,” Theoretical Computer Science,, vol.337, pp.370-378, (2005).
[12] Sun-Yuan Hsieh, Tzu-Hsiung Shen, “Edge-bipancyclicity of a hypercube with faulty vertices and edges,” Discrete Applied Mathematics , vol. 156, pp.1802-1808, (2008).
[13] Chun-Nan Hung, Y. H. Chang, and C. M. Sun, “Longest paths and cycles in fault hypercubes,” Proceedings of the IASTED ICPDCN, pp.101-110, (2006).
[14] Chun-Nan Hung and Guan-Yu Shi, “Vertex fault tolerance for multiple spanning paths in hypercube,” Proceedings of the 24th Workshop on Combinatorial Mathematics and Computational Theory, pp.241-250, (2007).
[15] Tseng-Kuei Li , Chang-Hsiung Tsai , Jimmy J.M.Tan , and Lih-Hsing Hsu, “Bipanconnectivity and edge-fault-tolerant bipancyclicity of hypercubes,” Information Processing Letters, 87, pp.107-110, (2003).
[16] Meijie Ma, Guizhen Liu, Xiangfeng Pan, “Path embedding in faulty hypercubes,” Applied Mathematics and Computation, (2007).
[17] C. D. Park and K. Y. Chwa, “Hamiltonian properties on the class of hypercubelike networks,” Information Processing Letters, 91, pp.11-17, (2004).
[18] Abhijit Sengupta, “On ring embedding in hypercubes with faulty nodes and links,” Information Processing Letters, 68, pp.207-214, (1998).
[19] Wen-Yan Su and Chun-Nan Hung, “The longest ring embedding in faulty hypercube,” Proceedings of the 23rd Workshop on Combinatorial Mathematics and Computational Theory, pp.262-272, (2006).
[20] Y. C. Tseng, “Embedding a ring in a hypercube with both faulty links and faulty nodes,” Information Processing Letters, 59, pp.217-222, (1996).
[21] C. H. Tsai, J.J.M. Tan, T.Liang, and L.H. Hsu, “Fault-tolerant Hamiltonian laceability of hypercubes,” Information Processing Letters, 83, pp.301-306, (2002).
[22] Chang-Hsiung Tsai, “Fault-tolerant cycles embedded in hypercubes with mixed link and node failures,” Applied Mathematics Letters, 21, pp.855-860, (2008).
[23] Chang-Hsiung Tsai, “Cycles embedding in hypercubes with node failures,” Information Processing Letters, vol.102, pp.242-246, (2007).
[24] Y. C. Tseng, “Embedding a ring in a hypercube with both faulty links and faulty nodes,” Information Processing Letters, vol.59, pp.217-222, (1996).
[25] Aniruddha S. Vaidya, “A Class of Hypercube-like Networks,” Parallel and Distributed Processing, 1993. Proceedings of the Fifth IEEE Symposium, pp.800-803, (1993).
[26] Dajin Wang, “Embedding Hamiltonian Cycles into Folded Hypercubes with Faulty Links,” Journal of Parallel and Distributed Computing, vol.61, pp.545-564, (2001).
[27] Jun-Ming Xu, Zheng-Zhong Du, Min Xu, “Edge-fault-tolerant edge-bipancyclicity of hypercubes,” Information Processing Letters, vol.102, pp.146-150, (2005).
[28] J.-M. Xu, M.-J. Ma, Z.-Z. Du, “Edge-fault-tolerant properties of hypercubes and folded hypercubes,” Australasian Journal of Combinatorics, vol.35, pp. 7-16, (2006).
[29] Ming-Chien Yang, Tseng-Kuei Li, Jimmy J.M. Tan, Lih-Hsing Hsu, “Fault-tolerant cycle-embedding of crossed cubes,” Information Processing Letters, vol.88, pp.149-154 (2003).
[30] Ming-Chien Yang,Tseng-Kuei Li, Jimmy J.M. Tan, Lih-Hsing Hsu, “On embedding cycles into faulty twisted cubes,” Information Sciences, vol.176, pp.676-690 (2006).
[31] Ming-Chien Yang, Jimmy J.M. Tan, Lih-Hsing Hsu, “Highly fault-tolerant cycle embeddings of hypercubes,” Journal of Systems Architecture, vol.53, pp.227-232 (2007).
