Connectivity plays an important role in measuring the fault tolerance of interconnection networks. The g-good-neighbor connectivity of an interconnection network G is the minimum cardinality of g-good-neighbor cuts. Diagnosability of a multiprocessor system is one important study topic. A new measure for fault diagnosis of the system restrains that every fault-free node has at least g fault-free neighbor vertices, which is called the g-good-neighbor diagnosability of the system. As a famous topology structure of interconnection networks, the n-dimensional bubblesort star graph BS n has many good properties. In this paper, we prove that 2-good-neighbor connectivity of BS n is 8n − 22 for n ≥ 5 and the 2-good-neighbor connectivity of BS 4 is 8; the 2-good-neighbor diagnosability of BS n is 8n − 19 under the PMC model and MM * model for n ≥ 5.

Diagnosability of a multiprocessor system G is one important measure of the reliability of interconnection networks. In 2016, Zhang et al. proposed the g-extra diagnosability of G, which restrains that every component of G S − has at least ( )The locally twisted cube n LTQ is applied widely.In this paper, we show that n LTQ is tightly ( )and the 3-extra diagnosability of n LTQ under the PMC model and MM * model is 4 6 n − for 5 n ≥ and 7 n ≥ , respectively.