Reliability of DQcube Networks Under the Condition of r-Component

Connectivity is an important measure parameter to evaluate the fault tolerance of networks. With the continuous expansion of networks scale, it is inevitable that the processor fails. Once the processor fails, the information processed by the failed processor will be unreliable, which may cause fatal consequences. Therefore, it is of great significance to study the connectivity and diagnosability of networks. In this paper, we establish that the (r +1)-component connectivity of DQcube is ck(r+1)(DQ(m,d,n))= 1/2r(2) + (n + 1/2)r + 1, where n >= 2 and 1 <= r <= n. Furthermore, we determine that the (r + 1)-component diag nosability of DQcube is ct(r+1)(DQ(m, d, n)) = -1/2r(2) + (n - 1/2)r + n + 1 under the PMC model and the MM* model, where n >= 3 and 1 <= r <= n - 3.