We investigate the critical sets of reverse edge-magic labelings on graphs, especially star, and the application on secret sharing In this paper, we propose two-level secret sharing scheme based critical sets on a reverse edge magic labeling of star graphs. It is a scheme which creates two types of hierarchical sets. The first set contains share that are more powerful than the share in the second set. We name this scheme the departmental secret sharing scheme. These two secret sharing schemes are constructed by critical sets of reverse edge-magic labelling. We build banking secret sharing scheme that will share a secret among one bank manager and several sets of authorized staff members. © 2019 Author(s).