A New Measure for Locally t-Diagnosable Under PMC Model

PMC model is the test-based diagnosis which a vertex performs the diagnosis by testing the neighbor vertices via the edges between them. Hsu and Tan proposed two structures to diagnose a vertex. But these structures don't always exist for any vertex. Here, we propose a new testing structure to diagnose a vertex under PMC model to solve the problem above. It can fit more general networks. Let S be a set of faulty edges of the n-dimensional hypercube Q(n). Using this structure, we show that every vertex u of Q(n) is deg(Qn-S)(u)-diagnosable if delta(Q(n) - S) >= 2, deg(Qn-S)(x) + deg(Qn-S)(y) >= 5 for every two adjacent vertices x and y in Q(n) - S, and n >= 5.