The partial diagnosability of interconnection networks under the Hybrid PMC model.

System level diagnosis is a primary method to identify the faulty elements in a multiprocessor system. Different from the traditional system level fault diagnosis models, the new fault diagnosis model, hybrid PMC model (short for HPMC model), is suitable to the circumstances that the processor and link faults occur simultaneously. Under the HPMC model, the q-edge restricted diagnosability of a system H, denoted by tqe(H), is the maximum number p such that H can correctly identify all the faulty elements containing p faulty processors and at most q faulty links. Similarly, the p-vertex restricted edge-diagnosability of a system H, denoted by spv(H), is the maximum number q such that H can correctly identify all the faulty elements containing q faulty links and at most p faulty processors. These two diagnosability are collectively referred to as partial diagnosability. We investigate and determine the q-edge restricted diagnosability of a system H under the HPMC model for q≥η(H), where η(H)=max⁡{|N(u)∩N(v)||uv∈E(H)}. In addition, we investigate the relationship between tqe(H) and spv(H) under the HPMC model, and show that under some conditions, spv(H)=q if tqe(H)=p. Applying our results, the two kinds of partial diagnosability of k-ary n-cubes, bijective connection networks and undirected Kautz graphs are established.