TITLE:
Non-Inclusive 1-Good-Neighbor Diagnosability of Augmented Cubes
AUTHORS:
Wanlin Gan, Faye Geng, He Li
KEYWORDS:
Non-Inclusive Diagnosability, -Good-Neighbor, Augmented Cubes
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.14 No.1,
January
20,
2026
ABSTRACT: 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
(
A
Q
n
)=8n−27
for
n≥23
; under the MM* model,
t
N
1
(
A
Q
n
)=6n−17
for
n≥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≥2
or other network topologies.