1. An increased interest expressed by researchers in the study of graphene has been associated with two factors. First, owing to its unique properties, graphene has been widely used in nanoelectronics [1][2][3]. Sec ond, graphene represents an ideal system for the devel opment and verification of theoretical models, because this material has made it possible to use mass less fermions that have no analogues among the ele mentary particles. The latter circumstance has allowed observations of quantum electrodynamic effects in graphene, specifically the Klein tunneling [4,5], which has usually required the generation of strong fields.An important direction in the physics of graphene is the investigation of the electronic states of the graphene formed on the surface of metals and semi conductors (see, for example, [6][7][8][9][10][11][12]). Research interest in the properties of an epitaxial graphene on the surface of metals stems from the fact that metallic contacts are necessary for the fabrication of instru mental structures based on graphene, as well as for the experimental study of the properties of the graphene itself. Moreover, the catalytic growth of graphene on the surface of transition metals is one of the methods used for the preparation of the graphene. The majority of theoretical calculations in this direction have been performed using numerical methods in the framework of the density functional theory formalism. Apart from these computational techniques, the investigation of the "graphene-other electronic structure" system, where the other electronic structure is an adatom, a metal substrate, or a semiconductor substrate, can be performed using the approach based on model Hamil tonians of the Anderson-Newns [13,14] and Haldane-Anderson [15] types. This approach allows one to obtain analytical expressions that can be useful for various applications. In the framework of these models, Davydov [10-12] considered the electronic states of the epitaxial graphene formed on the surface of a metal or semiconductor substrate and investigated the charge exchange between the graphene and the substrate. In these studies, it was demonstrated that, in the framework of the aforementioned models, it is possible to obtain the adequate results.Investigation of the electronic states of graphene formed on the surface of low dimensional systems is of particular interest. This is associated with the possi bility of varying the properties of low dimensional structures and also with the fact that these low dimen sional structures can be used to fabricate solid state structures with controllable parameters [16][17][18][19][20], which, in turn, is interesting from the viewpoint of the possibility of producing a controlled effect on the elec tronic states of graphene. It should be noted, however, that the problem of investigation of the "graphenelow dimensional structure" system, as compared to the case of the "graphene-macroscopic structure" system, has a different aspect. The point is that the graphene and a low dimensional substr...