Hybrid fault diagnosis capability analysis of highly connected graphs

TL;DR

This paper investigates the fault diagnosis capabilities of highly connected graphs, specifically focusing on the $h$-edge tolerable diagnosability, and provides new bounds and exact values for maximally connected graphs under different diagnostic models.

Contribution

It establishes the $h$-edge tolerable diagnosability for maximally connected graphs, extending previous results under the PMC and MM* models.

Findings

Derived lower bounds for $h$-edge tolerable diagnosability.

Established exact diagnosability for maximally connected graphs.

Extended previous theoretical results in graph diagnosability.

Abstract

Zhu et al. [Theoret. Comput. Sci. 758 (2019) 1--8] introduced the $h$-edge tolerable diagnosability to measure the fault diagnosis capability of a multiprocessor system with faulty links. This kind of diagnosability is a generalization of the concept of traditional diagnosability. A graph is called a maximally connected graph if its minimum degree equals its vertex connectivity. It is well-known that many irregular networks are maximally connected graphs and the $h$-edge tolerable diagnosabilities of these networks are unknown, which is our motivation for research. In this paper, we obtain the lower bound of the $h$-edge tolerable diagnosability of a $t$-connected graph and establish the $h$-edge tolerable diagnosability of a maximally connected graph under the PMC model and the MM$^*$ model, which extends some results in [IEEE Trans. Comput. 23 (1974) 86--88], [IEEE Trans. Comput. 53 (2004) 1582--1590] and [Theoret. Comput. Sci. 796 (2019) 147--153].