Equal relation between [formula omitted]-good-neighbor diagnosability under the PMC model and [formula omitted]-good-neighbor diagnosability under the MM[formula omitted] model of a graph

Abstract

Diagnosability has played an important role in reliability of an interconnection network. In 2012, Peng et al. proposed a new measure of diagnosability, namely, g-good-neighbor diagnosability, which requires every fault-free vertex has at least g fault-free neighbors. The PMC model and MM∗ model are widely adopted as the fault diagnosis model. The problems of g-good-neighbor diagnosability of many well-known networks under the PMC model and MM∗ model have been widely explored. In this paper, we study the relationship between g-good-neighbor diagnosability under the PMC model and g-good-neighbor diagnosability under the MM∗ model of a graph G. In addition, we give some sufficient conditions to ascertain g-good-neighbor diagnosability of a graph G under the PMC model and MM∗ model. From this, many previous results can be directly obtained and g-good-neighbor diagnosability for many well-known networks under the PMC model and MM∗ model, are derived.