Due to controversial reports concerning antibacterial activity of different graphene based materials it is very important to investigate their antibacterial action on a wide range of Gram-positive and Gram-negative bacteria. In this paper we have investigated the structure induced phototoxic antibacterial activity of four types of graphene based materials: graphene oxide (GO), graphene quantum dots (GQDs), carbon quantum dots (CQDs) and nitrogen doped carbon quantum dots (N-CQDs). Antibacterial activity was tested on 19 types of bacteria. It is found that nanometer-size CQDs and N-CQDs are the most potent agents whereas micrometer-size GO has very poor antibacterial activity. Electron paramagnetic resonance measurements confirmed photodynamic production of singlet oxygen for all types of used quantum dots. Detailed analysis has shown that N-CQDs are an excellent photodynamic antibacterial agent for treatment of bacterial infections induced by Enterobacter aerogenes (E. aerogenes), Proteus mirabilis (P. mirabilis), Staphylococcus saprophyticus (S. saprophyticus), Listeria monocytogenes (L. monocytogenes), Salmonella typhimurium (S. typhimurium) and Klebsiella pneumoniae.