Non-inclusive g-extra diagnosability of interconnection networks under PMC model

System level fault diagnosis theory is of great weight in the design and maintenance of multiprocessor systems. In this paper, we propose a novel kind of diagnosability, called non-inclusive g-extra diagnosability, that requires all faulty sets to be non-inclusive and every connected fault-free subgraph has at least $g+1$ vertices. Furthermore, we determine the non-inclusive g-extra diagnosability of a class of graphs under PMC model. As applications, the non-inclusive g-extra diagnosability of $(n,k)$-star graph $S_{n,k}$, data center networks DCell ($D_{k,n}$), BCDC ($B_n$) and BCube ($B{C}_{n,k}$) under PMC model are determined successively.