The diagnosability of multiprocessor systems under the enhanced comparison model

Diagnosability of a multiprocessor system $G$ is a fundamental topic. The $g$-extra diagnosability of $G$ requires that every fault-free component in $G-F$ has at least $g+1$ vertices, while the $g$-good-neighbor diagnosability requires that every fault-free vertex has at least $g$ fault-free neighbors. In this paper, we first propose a new model, the enhanced comparison (EC) model on $G$, and establish the relationship between the $g$-extra diagnosability and the $g$-good-neighbor diagnosability of $G$. Second, we present and prove necessary and sufficient conditions for the $g$-extra diagnosability of $G$, and determine the $g$-extra diagnosability of the hyper Petersen network. Finally, we present and prove necessary and sufficient conditions for the $g$-good-neighbor diagnosability of $G$, and determine the $g$-good-neighbor diagnosability of the star graph.