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Diagnosability of the Mobius cubes

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1 Author(s)
Jianxi Fan ; Dept. of Comput. Sci., Qingdao Inst. of Chem. Technol., Shandong, China

The recently introduced interconnection networks, the Mobius cubes, are hypercube variants that have some better properties than hypercubes. The n-dimensional Mobius cube Mn is a regular graph with 2n nodes and n2n-1 edges. The diameter of Mn is about one half that of the n-dimensional hypercube Q n and the average number of steps between nodes for Mn is about two-thirds of the average for Qn, and 1-Mn has dynamic performance superior to that of Qn. Of course, the symmetry of Mn is not superior to that of Qn, i.e., Qn is both node symmetric and edge symmetric , whereas Mn is, in general, neither node symmetric (n⩾4) nor edge symmetric (n⩾3). In this paper, we study the diagnosability of Mn. We use two diagnosis strategies, both based on the so-called PMC diagnostic model-the precise (one-step) diagnosis strategy proposed by Preparata et al. (1967) and the pessimistic diagnosis strategy proposed by Friedman (1975). We show that the diagnosability of Mn is the same as that of Qn , i.e., Mn is n-diagnosable under the precise diagnosis strategy and (2n-2)/(2n-2)-diagnosable under the pessimistic diagnosis strategy

Published in:

IEEE Transactions on Parallel and Distributed Systems  (Volume:9 ,  Issue: 9 )