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Processor fault diagnosis plays an important role in measuring the reliability of multiprocessor systems and the diagnosis of many well-known interconnection networks. The conditional diagnosability, which is more general than the classical diagnosability, is to measure the diagnosability of a multiprocessor system under the assumption that all of the neighbors of any node in the system cannot fail at the same time. This study shows that the conditional diagnosability for k-ary n-cubes under the PMC model is 8n−7 for k ≥ 4 and n ≥ 4.

The -star graph, denoted by , is an enhanced version of -dimensional star graphs , that has better scalability than , and possesses several good properties, compared with hypercubes. Diagnosis has been one of the most important issues for maintaining multiprocessor-system reliability. Conditional diagnosability, which is more general than classical diagnosability, measures the multiprocessor-system diagnosability under the assumption that all neighbors of any processor in the system cannot fail simultaneously. In this paper, we investigate the conditional diagnosability of for ( and ) and ( and ) under the comparison diagnosis model. Index Terms-Comparison diagnosis model, conditional diagnosability, diagnosability,-star graphs, multiprocessor systems. Acronyms and Abbreviations: PMC Preparata, Metze, Chien MM Maeng, Malek MM Maeng, Malek (a special case of the MM model) Notations: a simple graph with the vertex set , and edge set the vertex set of the edge set of the number of elements in the set the set of all vertices adjacent to in the degree of in (i.e., the number of vertices adjacent to in ) the graph obtained by deleting all the vertices in from Manuscript

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