  The Closed Cluster method (CC method) is applied to find solutions for
various calculation problems of the energy band structure of graphene. The
essence of the CC method consists in the addition of closing bonds between edge
atoms to the usual cluster method in order to eliminate the "dangling" bonds on
the edges of the cluster. We study the cases of an "infinite" layer of graphene
as well as nanoribbons, nanotubes and bilayer graphene. Results for these cases
are in agreement to that what was obtained by means of other methods (tight
binding approximation and others). By means of the CC method we also study the
problem of point defects in graphene and obtain the distortion of the energy
spectrum. The energy spectrum of the layer C$_{1-x}$ Si$_{x}$ $(0\leq x \leq
1)$ is found as well as the dependence of the energy gap on the concentration
of silicon. We show that the energy band structure of C$_{1-x}$ Si$_{x}$ looks
like a tunnel transition. Wave functions of graphene in the symmetry points of
Brillouin zone are also obtained.
