In this paper we present a comparative study of the magneto-optical properties of quasi-two-dimensional electrons in a graphene-like semiconductor superlattice composed of circular and elliptical quantum dots. The effect of transverse magnetic field on the band structure and absorption coefficient of the considered structures is studied. To this end a complete set of orthogonal basis functions is constructed in the symmetric gauge of the vector potential. This basis reflects both the periodicity of the system and magnetic phase effects due to the translations between the sites of the superlattice. Our calculations indicate on a topological change in the miniband structure due to the ellipticity of the quantum dots, and non-trivial modifications of the electron energy dispersion surfaces in the reciprocal space with the change of the number of magnetic flux quanta through the unit cell of the superlattice. The obtained results indicate the opportunity for an effective control of the magnetic and optical characteristics of honeycomb arrays of QDs through geometry effects and external magnetic field.