We present a theoretical study of the localized aspects of the alkali-metal atoms (Li, Na, K) interacting with graphene. We use an ab-initio calculation of the Hamiltonian parameters where the chemical properties of the interacting atoms (alkali and C), and the extended features of the electronic band structure of the solid are considered. Adatoms with a s-type valence orbital where the electron repulsion (U) in the atom assumes a finite value are considered. Three possible configuration states are analyzed: zero, one (spin up or down), and two electrons in the valence state. We describe the surface-atom interaction by projecting the Anderson Hamiltonian on the subspace of these atomic configurations, and introduced the Green's functions required to calculate the magnitudes of interest. Physical quantities of interest such as hybridization function, the adatom spectral density and transferred charge are obtained. We find that the interaction of alkali-metal atoms with graphene involves several atoms of the solid due to the extension of the s-type alkali atomic state and C atomic states. Charge is mostly transferred from the adatom towards the graphene sheet. (C) 2018 Elsevier B.V. All rights reserved.