Diagnosability of the Möbius Cubes

The recently introduced interconnection networks, the Mobius cubes, are hypercube variants that have some better properties than hypercubes. The n-dimensional Mobius cube M/sub n/ is a regular graph with 2/sup n/ nodes and n2/sup n-1/ edges. The diameter of M/sub n/ is about one half that of the n-dimensional hypercube Q/sub n/ and the average number of steps between nodes for M/sub n/ is about two-thirds of the average for Q/sub n/, and 1-M/sub n/ has dynamic performance superior to that of Q/sub n/. Of course, the symmetry of M/sub n/ is not superior to that of Q/sub n/, i.e., Q/sub n/ is both node symmetric and edge symmetric , whereas M/sub n/ is, in general, neither node symmetric (n/spl ges/4) nor edge symmetric (n/spl ges/3). In this paper, we study the diagnosability of M/sub n/. 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 M/sub n/ is the same as that of Q/sub n/, i.e., M/sub n/ is n-diagnosable under the precise diagnosis strategy and (2n-2)/(2n-2)-diagnosable under the pessimistic diagnosis strategy.