We analyze the influence of the charge and the degree of oxidation of the surface of graphene (Gr) on its interaction with cytosine and oligonucleotide r(C)(10). This is a computational study involving DFT calculations and molecular dynamics simulations. It is shown that cytosine interacts stronger with graphene oxide (GO) than with Gr, while the energy of the interaction of cytosine with GO only weakly depends on the degree of the Gr oxidation. A correlation between the shifts of vibrational frequencies of cytosine due to complexation with GO and the degree of the Gr oxidation is found. The adsorption of anionic oligonucleotide r(C)(10)onto neutral and positively charged surfaces has a certain conformational similarity to conformations formed with similar van der Waals interactions. Also, for charged surfaces, the Coulombic attraction gives a noticeable contribution to the total interaction energy. For a negatively charged graphene surface the electrostatic repulsion between Gr surface and negatively charged phosphate backbone of oligonucleotide weakens the total binding energy. Competition between the Coulombic repulsion and the van der Waals attraction results in formation of a unique oligonucleotide conformation where all 10 cytosines are stacked onto Gr.