Fault-tolerant panconnectivity of augmented cubes

doi:10.1007/s11464-009-0042-4

Front. Math. China

2009, Vol. 4

Issue (4) : 697-719 https://doi.org/10.1007/s11464-009-0042-4

Research articles

Fault-tolerant panconnectivity of augmented cubes

Hailiang WANG,Jianwei WANG,Jun-Ming XU,

Department of Mathematics, University of Science and Technology of China, Hefei 230026, China;

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Abstract The augmented cube AQ_n is a variation of the hypercube Q_n. This paper considers the panconnectivity of AQ_n (n

Keywords Path pancyclic hamiltonian connected panconnectivity augmented cube fault tolerance

Issue Date: 05 December 2009

Cite this article:

Hailiang WANG,Jun-Ming XU,Jianwei WANG. Fault-tolerant panconnectivity of augmented cubes[J]. Front. Math. China, 2009, 4(4): 697-719.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-009-0042-4
https://academic.hep.com.cn/fmc/EN/Y2009/V4/I4/697

	Chen Y-Y, Duh D-R, Ye T-L, Fu J-S. Weak-vertex-pancyclicityof (n, k)- star graphs. TheoreticalComputer Science, 2008, 396(3): 191―199 doi: 10.1016/j.tcs.2008.01.035
	Choudum A A, Sunitha V. Augmented cubes. Networks, 2002, 40(2): 71―84 doi: 10.1002/net.10033
	Choudum S A, Sunitha V. Distance and short parallelpaths in augmented cubes. Electronic Notesin Discrete Mathematics, 15(66) (electronic). Electron Notes DiscreteMath, 15, Amsterdam: Elsevier, 2003
	Fu J-S. Fault-free hamiltonian cycles in twisted cubes with conditional linkfaults. Theoretical Computer Science, 2008, 407(1―3): 318―329 doi: 10.1016/j.tcs.2008.06.024
	Hsieh S-Y. Embedding longest fault-free paths onto star graphs with more vertexfaults. Theoretical Computer Science, 2005, 337(1―3): 370―378 doi: 10.1016/j.tcs.2005.01.018
	Hsieh S-Y, Chen G-H, Ho C-W. Longest fault-free paths in star graphs with vertex faults. Theoretical Computer Science, 2001, 262: 215―227 doi: 10.1016/S0304-3975(00)00190-0
	Hsu H-C, Chiang L-C, Tan J J M, Hsu L-H. Fault hamiltonicityof augmented cubes. Parallel Computing, 2005, 31(1): 131―145 doi: 10.1016/j.parco.2004.10.002
	Hsu H-C, Lai P-L, Tsai C-H. Geodesic pancyclicity and balanced pancyclicity of augmentedcubes. Information Processing Letters, 2007, 101: 227―232 doi: 10.1016/j.ipl.2006.10.013
	Lin C-K, Huang H-M, Hsu L-H. The super connectivity of the pancake graphs and thesuper laceability of the star graphs. TheoreticalComputer Science, 2005, 339(2-3): 257―271 doi: 10.1016/j.tcs.2005.02.007
	Ma M-J, Liu G-Z, Xu J-M. Panconnectivity and edge-fault-tolerant pancyclicityof augmented cubes. Parallel Computing, 2007, 33(1): 36―42 doi: 10.1016/j.parco.2006.11.008
	Ma M-J, Liu G-Z, Xu J-M. Fault-tolerant embedding of paths in crossed cubes. Theoretical Computer Science, 2008, 407(1-3): 110―116 doi: 10.1016/j.tcs.2008.05.002
	Ma M-J, Liu G-Z, Xu J-M. The super connectivity of augmented cubes. Information Processing Letters, 2008, 106(2): 59―63
	Park J-H, Chwa K-Y. Recursive circulants andtheir embeddings among hypercubes. TheoreticalComputer Science, 2000, 244: 35―62 doi: 10.1016/S0304-3975(00)00176-6
	Park J H, Kim H C, Lim H S. Panconnectivity and pancyclicity of hypercube-like interconnectionnetworks with faulty elements. TheoreticalComputer Science, 2007, 377(1-3): 170―180 doi: 10.1016/j.tcs.2007.02.029
	Tsai C H, Linear array and ring embeddings in conditional faulty hypercubes. Theoretical Computer Science, 2004, 314(3): 431―443 doi: 10.1016/j.tcs.2004.01.035
	Tsai P-Y, Fu J-S, Chen G-H. Edge-fault-tolerant Hamiltonicity of pancake graphs underthe conditional fault model. TheoreticalComputer Science, 2008, 409(3): 450―460 doi: 10.1016/j.tcs.2008.09.015
	Tsai P-Y, Fu J-S, Chen G-H. Fault-free longest paths in star networks with conditionallink faults. Theoretical Computer Science, 2009, 410(8-10): 766―775 doi: 10.1016/j.tcs.2008.11.012
	Wang W-W, Ma M-J, Xu J-M. Fault-tolerant pancyclicity of augmented cubes. Information Processing Letters, 2007, 103(2): 52―56 doi: 10.1016/j.ipl.2007.02.012
	Xu J-M. Topological Structure and Analysis of Interconnection Networks. Dordrecht/Boston/London: Kluwer Academic Publishers, 2001
	Xu J-M, Ma M-J. A survey on cycle and pathembedding in some networks. Front MathChina, 2009, 4(2): 217―252 doi: 10.1007/s11464-009-0017-5
	Xu M, Xu J-M. The forwarding indices ofaugmented cubes. Information ProcessingLetters, 2007, 101(5): 185―189 doi: 10.1016/j.ipl.2006.09.013

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