The cyclic diagnosability of star graphs under the PMC and MM* models

Abstract

Although traditional connectivity and diagnosability have become relatively mature in assessing the reliability of multiprocessor systems, they often inadequately capture specific nuanced characteristics of these systems. In order to achieve a more comprehensive evaluation of the diagnostic capability of interconnection networks, Zhang et al. introduced a novel metric termed cyclic diagnosability. Within a system $G$, the cyclic diagnosability of $G$ represents the maximum cardinality of a faulty vertex set $F$ that can be self-diagnosed, provided that $G-F$ is disconnected and encompasses at least two cycles, with each cycle belonging to a different component. This paper presents an analysis of the structural properties of star graphs. Additional, we ascertain that the cyclic diagnosability of the $n$-dimensional star graph is $7n-20$, under PMC model and MM* model for $n\ge 13$. The size is nearly seven times that of the traditional diagnosability of star graphs.