By means of an envelope function analysis, we perform a numerical investigation of the conductance behavior of a graphene structure consisting of two regions (dots) connected to the entrance and exit leads through constrictions and separated by a potential barrier. We show that the conductance of the double dot depends on the symmetry of the structure and that this effect survives also in the presence of a low level of disorder, in analogy of what we had previously found for a double dot obtained in a semiconductor heterostructure. In graphene, this phenomenon is less dramatic and, in particular, conductance is not enhanced by the addition of symmetric constrictions with respect to that of the barrier alone.
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