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In this paper, a series of advances in elastic graph matching for facial expression recognition are proposed. More specifically, a new technique for the selection of the most discriminant facial landmarks for every facial expression (discriminant expression-specific graphs) is applied. Furthermore, a novel kernel-based technique for discriminant feature extraction from graphs is presented. This feature extraction technique remedies some of the limitations of the typical kernel Fisher discriminant analysis (KFDA) which provides a subspace of very limited dimensionality (i.e., one or two dimensions) in two-class problems. The proposed methods have been applied to the Cohn-Kanade database in which very good performance has been achieved in a fully automatic manner.