Non-inclusive g -good-neighbor diagnosability of Hypercubes

In order to better measure the fault tolerance and reliability of a network, Yuan et al. introduced the non-inclusive g-good-neighbor diagnosability of a network. The g-good-neighbor faulty set is a special faulty set, which satisfies that every fault-free vertex has at least g fault-free neighbors. The non-inclusive g-good-neighbor diagnosability requires every pair of g-good-neighbor faulty sets is non-inclusive, denoted as tNg(G). In the paper, we study the non-inclusive g-good-neighbor diagnosability of hypercubes, and obtain tNg(Qn)=(n−1−g)2g+1+2g−1 for g∈{1,2} under the PMC model, tN1(Qn)=3n−5, tN2(Qn)=8n−21 under the MM* model.