Publication 2006 Issue No. 7 - July Abstract - Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges
Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges
July 2006 (vol. 55 no. 7)
pp. 854-863
 ASCII Text x Sun-Yuan Hsieh, Nai-Wen Chang, "Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges," IEEE Transactions on Computers, vol. 55, no. 7, pp. 854-863, July, 2006.
 BibTex x @article{ 10.1109/TC.2006.104,author = {Sun-Yuan Hsieh and Nai-Wen Chang},title = {Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges},journal ={IEEE Transactions on Computers},volume = {55},number = {7},issn = {0018-9340},year = {2006},pages = {854-863},doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2006.104},publisher = {IEEE Computer Society},address = {Los Alamitos, CA, USA},}
 RefWorks Procite/RefMan/Endnote x TY - JOURJO - IEEE Transactions on ComputersTI - Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty EdgesIS - 7SN - 0018-9340SP854EP863EPD - 854-863A1 - Sun-Yuan Hsieh, A1 - Nai-Wen Chang, PY - 2006KW - Graph-theoretic interconnection networksKW - Möbius cubesKW - fault-tolerant embeddingKW - pancyclicityKW - Hamiltonian.VL - 55JA - IEEE Transactions on ComputersER -
A graph G=(V,E) is said to be pancyclic if it contains fault-free cycles of all lengths from 4 to |V| in G. Let F_{v} and F_{e} be the sets of faulty nodes and faulty edges of an n{\hbox{-}}{\rm dimensional} Möbius cube MQ_{n}, respectively, and let F=F_{v}\cup F_{e}. A faulty graph is pancyclic if it contains fault-free cycles of all lengths from 4 to |V-F_{v}|. In this paper, we show that MQ_{n}-F contains a fault-free Hamiltonian path when |F|\leq n-1 and n\geq 1. We also show that MQ_{n}-F is pancyclic when |F|\leq n-2 and n\geq 2. Since MQ_{n} is regular of degree n, both results are optimal in the worst case.

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Index Terms:
Graph-theoretic interconnection networks, M&#246;bius cubes, fault-tolerant embedding, pancyclicity, Hamiltonian.
Citation:
Sun-Yuan Hsieh, Nai-Wen Chang, "Hamiltonian Path Embedding and Pancyclicity on the Möbius Cube with Faulty Nodes and Faulty Edges," IEEE Transactions on Computers, vol. 55, no. 7, pp. 854-863, July 2006, doi:10.1109/TC.2006.104