The 2-good-neighbor connectivity and 2-good-neighbor diagnosability of bubble-sort star graph networks

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 bubble-sort star graph BSn has many good properties. In this paper, we prove that 2-good-neighbor connectivity of BSn is 8n−22 for n≥5 and the 2-good-neighbor connectivity of BS4 is 8; the 2-good-neighbor diagnosability of BSn is 8n−19 under the PMC model and MM∗ model for n≥5.