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Diagnosability of the Möbius Cubes
September 1998 (vol. 9 no. 9)
pp. 923-928

Abstract—The recently introduced interconnection networks, the Möbius cubes, are hypercube variants that have some better properties than hypercubes. The n-dimensional Möbius 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 Qn 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 [1]. Of course, the symmetry of Mn is not superior to that of Qn, i.e., Qn is both node symmetric and edge symmetric [11], whereas Mn is, in general, neither node symmetric (n≥ 4) nor edge symmetric (n≥ 3) [1]. 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. [10] and the pessimistic diagnosis strategy proposed by Friedman [9]. 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.

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Index Terms:
The Möbius cube, diagnosis, diagnosability, hypercube, multiprocessor system.
Jianxi Fan, "Diagnosability of the Möbius Cubes," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 9, pp. 923-928, Sept. 1998, doi:10.1109/71.722224
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