Understanding peptide-surface interactions is crucial for programming self-assembly of peptides at surfaces and in realizing their applications, such as biosensors and biomimetic materials. In this study, we developed insights into the dependence of a residue's interaction with a surface on its neighboring residue in a tripeptide using molecular dynamics simulations. This knowledge is integral for designing rational mutations to control peptide-surface complexes. Using graphene as our model surface, we estimated the free energy of adsorption (Delta A(ads)) and extracted predominant conformations of 26 tripeptides with the motif LNR - CR - Gly, where LNR and CR are variable left-neighboring and central residues, respectively. We considered a combination of strongly adsorbing (Phe, Trp, and Arg) and weakly adsorbing (Ala, Val, Leu, Ser, and Thr) amino acids on graphene identified in a prior study to form the tripeptides. Our results indicate that Delta A(ads), of a tripeptide cannot be estimated as the sum of Delta A(ads) of each residue indicating that the residues in a tripeptide do not behave as independent entities. We observed that the contributions from the strongly adsorbing amino acids were dominant, which suggests that such residues could be used for strengthening peptide-graphene interactions irrespective of their neighboring residues. In contrast, the adsorption of weakly adsorbing central residues is dependent on their neighboring residues. Our structural analysis revealed that the dihedral angles of LNR are more correlated with that of CR in the adsorbed state than in bulk state. Together with Delta A(ads) trends, this implies that different backbone structures of a given CR can be accessed for a similar Delta A(ads) by varying the LNR. Therefore, incorporation of context effects in designing mutations can lead to desired peptide structure at surfaces. Our results also emphasize that these cooperative effects in APl ads and structure are not easily predicted a priori. The collective results have applications in guiding rational mutagenesis techniques to control orientation of peptides at surfaces and in developing peptide structure prediction algorithms in adsorbed state from its sequence.