Fault-Tolerant Pancyclicity of the Mobius Cubes

Ming-Chien YANG  Tseng-Kuei LI  Jimmy J.M. TAN  Lih-Hsing HSU 

Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences  Vol.E88-A  No.1  pp.346-352
Publication Date: 2005/01/01
Online ISSN: 
Print ISSN: 0916-8508
Type of Manuscript: PAPER
Category: Graphs and Networks
Keyword: 
cycle embedding,  Mobius cube,  pancyclic,  hamiltonian,  fault tolerance, 

Full Text: PDF(289.8KB)

Summary: 
The Mobius cube MQn proposed by Cull et al. is an alternative to the popular hypercube network. Recently, MQn was shown to be pancyclic, i.e., cycles of any lengths at least four can be embedded into it. Due to the importance of the fault tolerance in the parallel processing area, in this paper, we study an injured MQn with mixed node and link faults. We show that it is (n - 2)-fault-tolerant pancyclic for n 3, that is, an injured n-dimensional MQn is still pancyclic with up to (n - 2) faults. Furthermore, our result is optimal.