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Issue No.11 - Nov. (2013 vol.62)
pp: 2337-2340
Qiang Zhu , Xidian University, Xi'an
Xin-Ke Wang , Xidian University, Xi'an
Guanglan Cheng , Xidian University, Xi'an
ABSTRACT
Reliability evaluation of interconnection network is important to the design and maintenance of multiprocessor systems. Extra connectivity determination and faulty networks' structure analysis are two important aspects for the reliability evaluation of interconnection networks. An $(n)$-dimensional bijective connection network (in brief, BC network), denoted by $(X_n)$, is an $(n)$-regular graph with $(2^{n})$ vertices and $(n2^{n-1})$ edges. The hypercubes, M$(\ddot{o})$bius cubes, crossed cubes, and twisted cubes are some examples of the BC networks. By exploring the boundary problem of the BC networks, we prove that when $(n\ge 4)$ and $(0\le h\le n-4)$ the $(h)$-extra connectivity of an $(n)$-dimensional BC network $(X_n)$ is $(\kappa_{h}(X_n)=)$ $(n(h+1)-{1\over 2} h(h+3))$. Furthermore, there exists a large connected component and the remaining small components have at most $(h)$ vertices in total if the total number of faulty vertices is strictly less its $(h)$-extra connectivity. As an application, the results on the $(h)$-extra connectivity and structure of faulty networks on hypercubes, M$(\ddot{o})$bius cubes, crossed cubes, and twisted cubes are obtained.
INDEX TERMS
Hypercubes, Multiprocessing systems, Computer network reliability, Program processors, Software reliability,interconnection networks, BC networks, reliability, maximally connected component, extra connectivity
CITATION
Qiang Zhu, Xin-Ke Wang, Guanglan Cheng, "Reliability Evaluation of BC Networks", IEEE Transactions on Computers, vol.62, no. 11, pp. 2337-2340, Nov. 2013, doi:10.1109/TC.2012.106
REFERENCES
[1] F. Harary, "Conditional Connectivity," Networks, vol. 143, no. 12, pp. 346-357, 1983.
[2] A. Esfahanian and S. Hakimi, "On Computing a Conditional Edge-Connectivity of a Graph," Information Processing Letters, vol. 27, pp. 195-199, Apr. 1988.
[3] F.T. Boesch, "Synthesis of Reliable Networks-A Survey," IEEE Trans. Reliability, vol. R-35, no. 3, pp. 240-246, Aug. 1986.
[4] A.H. Esfahanian, "Generalized Measures of Fault Tolerance with Application to $n$ -Cube Networks" IEEE Trans. Computers, vol. 38, no. 11, pp. 1586-1591, Nov. 1989.
[5] Y.-C. Chen, "Super Connectivity of K-Regular Interconnection Networks," Applied Math. and Computation, vol. 217, no. 21, pp. 8489-8494, Jul. 2011.
[6] M. Ma and L. Zhu, "The Super Connectivity of Exchanged Hypercubes," Information Processing Letters, vol. 111, no. 8, pp. 360-364, Mar. 2011.
[7] J.-M. Xu, M. Xu, and Q. Zhu, "The Super Connectivity of Shuffle-Cubes," Information Processing Letters, vol. 96, no. 4, pp. 123-127, Nov. 2005.
[8] J. Fabrega and M.A. Fiol, "Extra Connectivity of Graphs with Large Girth," Discrete Math., vol. 127, nos. 1-3, pp. 163-170, Mar. 1994.
[9] J. Fabrega and M.A. Fiol, "On the Extra Connectivity of Graphs," Discrete Math., vol. 155, pp. 49-57, Apr. 1996.
[10] W. Yang and J.X. Meng, "Extra Connectivity of Hypercubes," Applied Math. Letters, vol. 22, pp. 887-891, June 2009.
[11] J.M. Xu and Q. Zhu, "On Restricted Connectivity and Extra-Connectivity of Hypercubes and Folded Hypercubes," J. Shanghai Jiaotong Univ., vol. E-10, no. 2, pp. 203-207, 2005.
[12] J.-M. Xu, Q. Zhu, and M. Xu, "Fault-Tolerant Analysis of a Class of Networks," Information Processing Letters, vol. 103, no. 6, pp. 222-226, Apr. 2007.
[13] Q. Zhu, J.-M. Xu, X. Hou, and M. Xu, "On Reliability of the Folded Hypercubes," Information Sciences, vol. 177, no. 8, pp. 1782-1788, Apr. 2007.
[14] P. Cull and S. Larson, "The M$\ddot{o}$ bius Cubes," IEEE Trans. Computers, vol. 44, no. 5, pp. 647-659, May 1995.
[15] K. Efe, "A Variation on the Hypercube with Lower Diameter," IEEE Trans. Computers, vol. 40, no. 11, pp. 1312-1316, Nov. 1991.
[16] P.A.J. Hibers, M.R.J. Koopman, and J.V.D. Snepscheut, "The Twisted Cube," Proc. Conf. Parallel Architectures and Languages Europe, pp. 152-159, 1987.
[17] J. Fan and L. He, "BC Interconnection Networks And Their Properties," Chinese J. Computers, vol. 126, no. 1, pp. 84-90, May 1998.
[18] J. Fan and X. Jia, "Edge-Pancyclicity and Path-Embeddability of Bijective Connection Graphs" Information Sciences, vol. 178, no. 2, pp. 340-351, Jan. 2008.
[19] J. Fan and X. Lin, "The t/k-Diagnosability of the BC Graphs," IEEE Trans. Computers, vol. 54, no. 2, pp. 176-184, Feb. 2005.
[20] Q. Zhu, "On Conditional Diagnosability and Reliability of the BC Networks," J. Supercomputing, vol. 45, no. 2, pp. 173-184, Dec. 2008.
[21] G.-H. Hsu and J.M.T. Jimmy, "Conditional Diagnosability of the BC Networks under the Comparison Diagnosis Model," Proc. Int'l Computer Symp., vol. 1, pp. 269-274, Nov. 2008.
[22] J. Fan, "Diagnosability of the M$\ddot{o}$ bius Cubes," IEEE Trans. Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998.
[23] J.A. Bondy and U.S.R. Murty, Graph Theory with Applications. North Holland, 1976.
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