Non-Inclusive 1-Good-Neighbor Diagnosability of Augmented Cubes

The diagnosability of interconnection networks serves as a critical metric for evaluating the reliability of multiprocessor systems, as it quantifies the system’s capability to identify faulty processors. Among various diagnosability models, the non-inclusive $g$ -good-neighbor diagnosability offers a more precise characterization of fault tolerance by considering both the non-inclusive nature of fault sets and the requirement of maintaining a certain number of good neighbors for non-faulty vertices. This study focuses on the non-inclusive 1-good-neighbor diagnosability of augmented cubes ($A{Q}_n$ ), a class of interconnection networks with excellent topological properties. Through systematic analysis using structural construction, proof by contradiction, and induction, we derive the exact values of the non-inclusive 1-good-neighbor diagnosability of $A{Q}_n$ under two classic diagnosis models: under the PMC model, $t_{N_1}\left(A{Q}_n\right)=8n？27$ for $n\ge 23$ ; under the MM^* model, $t_{N_1}\left(A{Q}_n\right)=6n？17$ for $n\ge 13$ . These results provide valuable insights for the design and optimization of reliable multiprocessor systems, and lay a foundation for extending the research to $g\ge 2$ or other network topologies.