In this paper a generalized framework for face verification is proposed employing discriminant techniques in all phases of elastic graph matching. The proposed algorithm is called discriminant elastic graph matching (DEGM) algorithm. In the first step of the proposed method, DEGM, discriminant techniques at the node feature vectors are used for feature selection. In the sequel, the two local similarity values, i.e., the similarity measure for the projected node feature vector and the node deformation, are combined in a discriminant manner in order to form the new local similarity measure. Moreover, the new local similarity values at the nodes of the elastic graph are weighted by coefficients that are derived as well from discriminant analysis in order to form a total similarity measure between faces. The proposed method exploits the individuality of the human face and the discriminant information of elastic graph matching in order to improve the verification performance of elastic graph matching. We have applied the proposed scheme to a modified morphological elastic graph matching algorithm. All experiments have been conducted in the XM2VTS database resulting in very low error rates for the test sets.