Fault diagnosability of Bicube networks under the PMC diagnostic model

A network's fault diagnosability is the maximum number of nodes (or processors) that are allowed to fail, while still being able to be identified by analyzing the syndrome of mutual testing, under the well-known PMC diagnostic model. It is a crucial indicator of the network's reliability. The original definition of diagnosability is often too strict to realistically reflect a network's robustness, because it is limited by the network's minimum degree. To better measure the actual reliability, many variants of diagnosability have been proposed, with g-extra diagnosability being one of the most noticeable diagnostic strategies. In this paper, we determine both the diagnosability and g-extra diagnosability for Bicube BQ_n, a recently proposed variant of the classic hypercube. We first show that the diagnosability for BQ_n, the n-dimensional Bicube, is n; and then prove that the g-extra diagnosability for BQ_n is (g+1)n−g−(g2).