Fault diagnosability of arrangement graphs

The growing size of the multiprocessor system increases its vulnerability to component failures. It is crucial to locate and to replace the faulty processors to maintain a system’s high reliability. The fault diagnosis is the process of identifying faulty processors in a system through testing. In this paper, we show that the largest connected component of the survival graph contains almost all of the remaining vertices in the (n, k)-arrangement graph An,k when the number of moved faulty vertices is up to twice or three times the traditional connectivity. Using this fault resiliency, we establish the conditional diagnosability of An,k under the comparison model, and prove that the conditional diagnosability of An,k is (3k − 2)(n − k) − 3 for k ⩾ 4, n ⩾ k + 2; and the conditional diagnosability of An,n−1 is 3n − 7 for n ⩾ 5.