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Ruei-Yu Wu ^{1} and Dyi-Rong Duh^{2}**

Hwa Hsia Institute of Technology

Taipei Hsien, 235 Taiwan

National Chi Nan University

Nantou Hsien, 545 Taiwan

Sarbazi-Azad, Ould-Khaoua, and Mackenzie proved in 2001 that there exists a Hamiltonian cycle in a pyramid network and they also constructed a Hamiltonian path between apex and each of 4 frontiers of a pyramid network. The fault tolerance is a crucial matter for parallel computing, especially in a large network. This work improves Sarbazi-Azad et al.¡¦s result and considers other relative problems in pyramid networks such as the fault tolerant Hamiltonian problem and the Hamiltonian-connected problem. The problem of finding Hamiltonian cycles in a pyramid network with one faulty node (link) is investigated. Additionally, the Hamiltonian-connectedness of a pyramid network can be shown by constructing a Hamiltonian path between any two distinct nodes in it.

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Keywords:
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pyramid networks, Hamiltonian cycle, Hamiltonian-connectedness, fault tolerance,
interconnection networks

Retrieve PDF document (**200903_12.pdf**)

Received May 14, 2007; revised September 19, 2007 & March 18, 2008; accepted April 17, 2008.

Communicated by Tsan-sheng Hsu.
^{*} This work was also partially supported by the National Science Council of Taiwan, R.O.C. under contract
No. NSC 91-2213-E-260-003-.