During this thesis project research, there were collected experimental data regarding interactions of individual DNA molecules with monolayer graphene and develop a breakthrough model to explain data. Moreover, there were investigated the fundamental interactions involved when individual single-stranded DNA molecules and underlying graphene surface are in contact and when they mutually detach. For that purpose, it was used Single-Molecule Force Spectroscopy (SMFS) with the help Atomic Force Microscope (AFM). Force vs distance curves have been collected inside the liquid environment, which shows characteristic force plateaus once individual molecules are peeled off from the surface. Plateaus that correspond to desorption of last individual DNA molecule near AFM tip apex are statistically analyzed after experiments, with our data collected into histograms which are fitted with appropriate Gaussian curves.