Kermeta is a meta-language for specifying the structure and behavior of graphs of interconnected objects called models. In this paper, we show that Kermeta is relatively suitable for solving three graph-based problems. First, Kermeta allows the specification of generic model transformations such as refactorings that we apply to different metamodels including Ecore, Java, and Uml. Second, we demonstrate the extensibility of Kermeta to the formal language Alloy using an inter-language model transformation. Kermeta uses Alloy to generate recommendations for completing partially specified models. Third, we show that the Kermeta compiler achieves better execution time and memory performance compared to similar graph-based approaches using a common case study. The three solutions proposed for those graph-based problems and their evaluation with Kermeta according to the criteria of genericity, extensibility, and performance are the main contribution of the paper. Another contribution is the comparison of these solutions with those proposed by other graph-based tools.