Hybrid diagnosis of regular networks under the HPMC fault model

Abstract

Faulty diagnosis of multiprocessor systems is an important area of study in the design and maintenance of multiprocessor systems. However, most researchers on diagnosability focus on vertex faults. In real circumstances, not only vertex faults take place but also edge malfunctions may occur. Recently, a kind of new model for the fault diagnosis in hybrid fault circumstances with both vertex and edge faults, called the HPMC model, has been proposed. Moreover, two new measures for fault diagnosis of multiprocessor systems in hybrid fault circumstances, namely, the h-restricted vertex diagnosability and the r-restricted edge diagnosability, denoted by $t_{h}^{e}(G)$ and $s_{r}^{v}(G)$, respectively, have been proposed under the HPMC model at the same time. In this paper, we obtain the h-restricted vertex diagnosability and the r-restricted edge diagnosability of some classes of regular networks under the HPMC model, which extend some results in Zhu et al. (AKCE Int J Graphs Comb 17(3):755–760, 2020).