Diagnosability of the Mobius 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_n is a regular graph with 2ⁿ nodes and n2^n-1 edges. The diameter of M_n is about one half that of the n-dimensional hypercube Q _n and the average number of steps between nodes for M_n is about two-thirds of the average for Q_n, and 1-M_n has dynamic performance superior to that of Q_n. Of course, the symmetry of M_n is not superior to that of Q_n, i.e., Q_n is both node symmetric and edge symmetric , whereas M_n is, in general, neither node symmetric (n⩾4) nor edge symmetric (n⩾3). In this paper, we study the diagnosability of M_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_n is the same as that of Q_n , i.e., M_n is n-diagnosable under the precise diagnosis strategy and (2n-2)/(2n-2)-diagnosable under the pessimistic diagnosis strategy