# The $h$-edge tolerable diagnosability of balanced hypercubes

## TL;DR

This paper determines the $h$-edge tolerable diagnosability of balanced hypercubes under two models, extending the understanding of fault diagnosis capabilities in multiprocessor systems with faulty links.

## Contribution

It completely characterizes the $h$-edge tolerable diagnosability of balanced hypercubes under PMC and MM* models, complementing previous results.

## Key findings

- Exact $h$-edge tolerable diagnosability values for $BH_n$
- Traditional diagnosability of $BH_n$ derived from these results
- Enhanced understanding of fault diagnosis in multiprocessor systems

## Abstract

To measure the fault diagnosis capability of a multiprocessor system with faulty links, Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1--8] introduced the $h$-edge tolerable diagnosability. This kind of diagnosability is a generalization of the concept of traditional diagnosability. In this paper, as complement to the results in [Theoret. Comput. Sci. 760 (2019) 1--14], we completely determine the $h$-edge tolerable diagnosability of balanced hypercubes $BH_n$ under the PMC model and the MM$^*$ model. Thus, the traditional diagnosability of $BH_n$ is also determined.