Adding impurities or doping through adsorption is an effective way to modify the properties of graphene-based materials. The capability of making predictions pertinent to the trends of elemental adsorption on graphene is very instrumental towards a better understanding of the more complex adsorption cases. It also affords useful guidelines for fabricating 2-D graphene materials with novel properties. The electronic structure of elemental adsorption on graphene is affected by side of adsorption (single- or double-sided), site of adsorption (i.e. bridge, hollow or top), and the relative orientation of the adsorbed sites (i.e. zigzag or armchair). In this contribution, we apply density functional theory (DFT) calculations to investigate the electronic structures of halogens (F, Cl, Br, I) adsorbed on graphene at lower concentrations spanning 1:6, 1:8 and 1:18 atomic ratios, in order to elucidate effects of adsorption trends. We demonstrate that adsorption of F is merely site-dependent (top). On the contrary, adsorptions of Cl, Br and I display a minimal dependence towards orientation (i.e. the effects of the deployed supercells). Our findings provide a deeper understanding of the elemental adsorption on graphene in terms of geometry which may aid in reexamining previous studies and producing better predictions for future studies, in which the inclusion of orientation is indispensable.