In this paper we propose a new graph formulation for solving Discrete Tomography problems in the case where only a very few number of projections are available. Graph formulations are efficient to solve many different pixel labeling problems in Image Processing. However, applying graph models for Discrete Tomography problems is a very challenging task due to the high dimensionality of the data and the complexity of the constraints formulations. Due to the NP-hardness of the problem, even the computation of a local minima is still a challenge. In this paper, we propose a graph model with a polynomial number of additional edges formulating the projection consistency and an iterative algorithm to efficiently minimize the energy function. Our formulation aims to provide 3D results based on a restricted number of projections.