The diagnosability is an important measure of the reliability of a multiprocessor system. Multiprocessor systems usually take interconnection networks (or graphs) as underlying topologies, and the n-dimensional star graph \(S_{n}\) is one of the most attractive interconnection networks of large scale multiprocessor systems. In order to better measure the reliability of a system, Zhang et al. introduced the non-inclusive h-extra diagnosability, which requires each component has at least \(h+1\) vertices after removing the fault vertex set. In this paper, we determine the non-inclusive h-extra diagnosability of star graphs under the PMC model and \(MM^{*}\) model, where \(h=1,2,3\) .
