Conditional Diagnosability of Alternating Group Networks Under the PMC Model

Fault diagnosis of processors has played an essential role when evaluating the reliability of multiprocessor systems. In many novel multiprocessor systems, their diagnosability has been extensively explored. Conditional diagnosability is a useful measure for evaluating diagnosability by adding a further condition that all neighbors of every node in the system do not fail at the same time. In this paper, we study the conditional diagnosability of n-dimensional alternating group networks ANn under the PMC model, and obtain the results t(c)(AN(4)) = 5, and t(c)(AN(n)) = 6n - 17 for n >= 5. In addition, for the isomorphism property between AN(n) and S-n,S- k with k = n - 2, namely (n, n - 2)-star graphs S-n,S- n (- 2), the above results can be extended to S-n,S- n - 2, and we have t(c)(S-4,S-2) = 5 and t(c)(S-n,S-n-2) = 6n - 17 for n >= 5. It is worth noting that the conditional diagnosability is about six times the degree of AN(n) and S-n,S- n-2, which is very different from general networks with a multiple of four.