Conditional diagnosability of multiprocessor systems based on complete-transposition graphs

Diagnosability is an important parameter to measure the ability of diagnosing faulty processors of a multiprocessor system. Conditional diagnosability is a realistic improvement of classical diagnosability under the condition that every processor has at least one fault-free neighboring processor. Complete-transposition graphs are proposed to be potential competitive network models of hypercubes as well as star graphs. In this paper, we show that the conditional diagnosability of the complete-transposition graph CTn under the MM∗ model is 32n(n−1)−6 for n≥7, while the conditional diagnosability of CTn under the PMC model is 2n(n−1)−9 for n≥5.