Relatively weak red photoluminescence of carbon dots (CDots) is a major challenge on the way to their successful implementation in biological and optoelectronic devices. We present a theoretical analysis of the interaction among the surface emission centers of CDots, showing that it may determine efficiency of the red photoluminescence of CDots. Based on the previous experimental studies, it is assumed that the optical response of the CDots is determined by the molecule-like subunits of polycyclic aromatic hydrocarbons (PAHs) attached to the CDots surface. Three characteristic types of coupling of these PAH subunits are considered: non-interacting monomers, noncovalently bound dimers, and covalently bound dimers with two, three, or four carbon linkers. We demonstrate that the CDots photoluminescence broadens, redshifts, and weakens by 2 orders of magnitude when the free monomers are substituted by the covalently bridged centers. These and other results of our study show that the realization of CDots with many weakly interacting surface emission centers may constitute an efficient way to achieve their efficient red photoluminescence, which is highly desirable for biological and optoelectronic applications.