Motivated by recent experimental and theoretical works dealing with the silicene and the graphene materials and inspired from the root systems of Lie algebras, we study the electronic and the magnetic properties of the iron adatom adsorption on the graphene. The calculations have been performed using the density functional theory method. More precisely, the system we consider here consists of a static single layer of the graphene interacting with the iron atoms which are placed at hollow (H) sites and localized at a distance Δ along the normal direction. This system, involving the G2 hexagons appearing in the classification of rank two Lie symmetries, exhibits, up some details, a nice double hexagonal symmetry required by coverage of 0.666 monolayer placed at H sites. The resulting materials behave like ferromagnetic ones having a strong spin polarization, instead of gapless-semiconductor with the nonmagnetic features appearing in the pure graphene. The responsible mechanism for such behaviors is the interaction between the iron atoms. It has been realized that there are two interaction types. The first one is associated with the direct interaction between the iron atoms, whereas the second one corresponds to the indirect interaction via the carbon atoms. Using the molecular field approximation, the Curie temperature has been estimated around 367 K. © 2013 Wiley Periodicals, Inc.