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Diagnosability is a key factor in the analysis of reliability for a network system. t/s-diagnosability is a novel measurement for evaluating the reliability of a system. In this paper, we derive some properties, which have not been reported by previous literatures, for a star network. By using these properties, we prove that an n-dimensional star graph (denoted by Sn) is [ln - (((l + 2)2)/3)]/([ln - (((l + 2)2)/3)] + l - 2)-diagnosable, where (n &#x2265; 5), 2 &#x2264; l &#x2264; n - 2. Furthermore, we prove that given an integer n(n ) 5), and another integer l(2 &#x2264; l &#x2264; n - 2), for some positive integer &#x03B2; &#x2208; ([(l - 1)n - (((l + 1)2)/3)], [ln - (((l + 2)2)/3)]], Sn is &#x03B2;/(&#x03B2; + l - 2)-diagnosable. In the last part of this paper, we propose an isolation-fast algorithm for Sn(n &#x2265; 5), and its time complexity is only O(N log2N), where N = n!.

Structural Properties and $t/s$ -Diagnosis for Star Networks Based on the PMC Model