The g-Good-Neighbor Conditional Diagnosability of Arrangement Graphs

A networks diagnosability is the maximum number of faulty vertices the network can discriminate solely by performing mutual tests among the vertices. It is an important measure of a network's robustness. The original diagnosability without any condition is often rather low because it is bounded by the network's minimum degree. Several conditional diagnosability have been proposed in the past to increase the allowed faulty vertices, and hence enhancing the diagnosability of the network. The g-good-neighbor conditional diagnosability is the maximum number of faulty vertices a network can guarantee to identify, under the condition that every fault-free vertex has at least fault-free neighbors (i.e., good neighbors). In this paper, we establish the g-good-neighbor conditional diagnosability for the (n, k)-arrangement graph network A(n,k). We will show that, under both the PMC model and the comparison model, the A(n,k)'s g-good-neighbor conditional diagnosability is [(g + 1)k - g](n - k), which can be several times higher than the A(n,k)'s original diagnosability.