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 Sn,k under the PMC model (2≤k≤n−1 and 1≤g≤n−k) and the comparison model (2≤k≤n−1 and 2≤g≤n−k) is n+g(k−1)−1, respectively. In addition, we derive that 1-good-neighbor diagnosability of Sn,k under the comparison model is n+k−2 for 3≤k≤n−1 and n≥4. As a supplement, we also derive that the g-good-neighbor diagnosability of the (n,1)-star graph Sn,1 (1≤g≤⌊n/2⌋−1 and n≥4) under the PMC model and the comparison model is ⌈n/2⌉−1, respectively.