Learning graph topology from data is challenging. Previous work leads to learning graphs on which the graph signals used for training are smooth. In this paper, we propose an optimization framework for learning multiple graphs, each associated to a class of signals, such that representation of signals within a class and discrimination of signals in different classes are both taken into consideration. A Fisher-LDA-like term is included in the optimization objective function in addition to the conventional Gaussian ML objective. A block coordinate descent algorithm is then developed to estimate optimal graphs for different categories of signals, which are then used to efficiently classify the different signals. Experiments on synthetic data demonstrate that our proposed method can achieve better discrimination between the learned graphs, leading to improvements in subsequent classification tasks.