The 3-extra conditional diagnosability of balanced hypercubes under MM∗ model

Diagnosis plays an important role in measuring the reliability of an interconnection network, and the diagnosability of interconnection networks has been widely investigated. For a system G, Zhang et al. introduced h-extra conditional diagnosability, denoted by th̃(G), which is a novel measure of diagnosability. In this paper, several new structural properties of balanced hypercubes have been derived. Based on these properties, the 3-extra conditional diagnosability of an n-dimensional balanced hypercube is determined to be t̃3(BHn)=4n−1 for n≥5 under the MM∗ model.