Fault-tolerant hamiltonicity and fault-tolerant hamiltonian connectivity of the folded Petersen cube networks

Authors:
Cheng-Kuan Lin;Tung-Yang Ho;Jimmy J. M. Tan;Lih-Hsing Hsu
Affiliations:
Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, Republic of China;Department of Industrial Engineering and Management, Ta Hwa Institute of Technology, Hsinchu, Taiwan, Republic of China;Department of Computer Science, National Chiao Tung University, Hsinchu, Taiwan, Republic of China;Department of Computer Science and Information Engineering, Providence University, Taichung, Taiwan, Republic of China
Venue:
International Journal of Computer Mathematics
Year:
2009

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Abstract

Some research on the folded Petersen cube networks have been published for the past several years due to its favourite properties. In this paper, we consider the fault-tolerant hamiltonicity and the fault-tolerant hamiltonian connectivity of the folded Petersen cube networks. We use FPQn, k to denote the folded Petersen cube networks of parameters n and k. In this paper, we show that FPQn, k-F remains hamiltonian for any F ⊆ V(FPQn, k)∪E(FPQn, k) with |F|≤n+3k-2 and FPQn, k-F remains hamiltonian connected for any F ⊆ V(FPQn, k)∪E(FPQn, k) with |F|≤n+3k-3 if (n, k)∉{(0, 1)}∪{(n, 0) | n is a positive integer}. Moreover, this result is optimal.