The g-good-neighbor diagnosability of (n, k)-star graphs.

Many large-scale multiprocessor or multi-computer systems take interconnection networks as underlying topologies. Fault diagnosis is especially important to identify fault tolerability of such systems. The g-good-neighbor (conditional) diagnosability such that every fault-free node has at least g fault-free neighbors is a novel measure of diagnosability. In this paper, we show that the g-good-neighbor diagnosability of the ( n , k ) -star graph S n , k under the PMC model ( 2 ź k ź n - 1 and 1 ź g ź n - k ) and the comparison model ( 2 ź k ź n - 1 and 2 ź g ź n - k ) is n + g ( k - 1 ) - 1 , respectively. In addition, we derive that 1-good-neighbor diagnosability of S n , k under the comparison model is n + k - 2 for 3 ź k ź n - 1 and n ź 4 . As a supplement, we also derive that the g-good-neighbor diagnosability of the ( n , 1 ) -star graph S n , 1 ( 1 ź g ź ź n / 2 ź - 1 and n ź 4 ) under the PMC model and the comparison model is ź n / 2 ź - 1 , respectively. We explore fault diagnosability of multiprocessor systems based on combinatorial network theory.We establish the g-good-neighbor diagnosability of the ( n , k ) -star graph S n , k under the PMC model.We establish the g-good-neighbor diagnosability of the ( n , k ) -star graph S n , k under the comparison model.