Extra diagnosability and good-neighbor diagnosability of -dimensional alternating group graph under the PMC model.

The h-extra diagnosability and g-good-neighbor diagnosability are two important diagnostic strategies at system-level that can significantly enhance the system's self-diagnosing capability. The h-extra diagnosability ensures that every component of the system after removing a set of faulty vertices has at least h+1 vertices. The g-good-neighbor diagnosability guarantees that after removing some faulty vertices, every vertex in the remaining system has at least g neighbors. In this paper, we analyze the extra diagnosability and good-neighbor diagnosability in a well-known n-dimensional alternating group graph AGn proposed for multiprocessor systems under the PMC model. We first establish that the 1-extra diagnosability of AGn (n≥5) is 4n−10. Then we prove that the 2-extra diagnosability of AGn (n≥5) is 6n−17. Next, we address that the 3-extra diagnosability of AGn (n≥5) is 8n−25. Finally, we obtain that the g-restricted connectivity and the g-good-neighbor diagnosability of AGn (n≥5) are (2g+2)n−2g+2−4+g and (2g+2)n−2g+2−4+2g for 1≤g≤2, respectively.