Triangular photonic crystal fibers with different core geometries have been investigated, in order to design single-mode large mode area fibers. In particular, 7-rod core fibers, obtained by removing the central air-hole and the first six surrounding ones in the transverse section, have been considered. By taking into account the leakage losses of the second-order mode, a phase diagram, which describes the boundary between the single-mode and multi-mode operation regimes, as well as the endlessly single-mode region, has been evaluated. Moreover, starting from this analysis, the cutoff normalized frequency has been calculated according to a formulation of the V parameter previously adopted for traditional 1-rod core triangular fibers. Simulation results have shown that, for a fixed air-filling fraction, 7-rod core triangular photonic crystal fibers are single-mode in a smaller wavelength range than 1-rod core ones. However, it is possible to obtain high effective area values, as well as single-mode operation, with 7-rod core fibers by considering low air-filling fractions and relatively small hole-to-hole distances.