Transition metal atom adsorption on graphene monolayers has been elucidated using periodic density functional theory under hybrid and generalized gradient approximation functionals. More specifically, we examined the adsorption of Cu, Fe, Zn, Ru, and Os on graphene monolayers by calculating, among others, the electronic density-of-states spectra of the adatom-graphene system and the overlap populations of the adatom with the nearest adsorbing graphene carbon atoms. These calculations reveal that Cu form primarily covalent bonds with graphene atoms via strong hybridization between the adatom orbitals and the sp band of the graphene substrate, whereas the interaction of the Ru and Os with graphene also contain ionic parts. Although the interaction of Fe with graphene atoms is mostly covalent, some charge transfer to graphene is also observed. The interaction of Zn with graphene is weak. Mulliken population analysis and charge contour maps are used to elucidate charge transfers between the adatom and the substrate. The adsorption strength is correlated with the metal adsorption energy and the height of the metal adatom from the graphene plane for the geometrically optimized adatom-graphene system. Our analysis shows that show that metal adsorption strength follows the adatom trend Ru approximate to Os > Fe > Cu > Zn, as verified by corresponding changes in the adsorption energies. The increased metal-carbon orbital overlap for the Ru relative to Os adatom is attributed to hybridization defects. (C) 2016 Elsevier B.V. All rights reserved.