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Diagnosability plays an important role in measuring the reliability of interconnection networks. Conditional faulty set is a special faulty set that does not contain all of neighbors of any vertex in a network. The conditional diagnosability is a metric that can give the maximum cardinality of the conditional faulty sets that the system is guaranteed to identify. This paper shows that the conditional diagnosability of the bubble-sort star graph B S n under the MM model is 6 n − 15 for n ≥ 6 and under the PMC model is 8 n − 21 for n ≥ 5 . [ABSTRACT FROM AUTHOR]