with numerous of unique properties [@Geim]. In section\[sec:essence\] the fundamental idea of the CC approach is presented as well as the rules for the construction of diagrams corresponding to the various clusters. In section\[sec:Ham\] examples of building Hamiltonian matrices and solutions for the secular equations in case of periodical structures without edges and defects are given. The aim of this section is to test our approach by means of comparison of the results with those obtained by other methods. In section\[sec:Bilayer graphene\] the CC approach is applied to bilayer graphene. In section\[sec:Wave functions\] we present wave functions at symmetry points of the Brillouin zone. In section\[sec:Nanoribbons and nanotubes\] we study nanoribbons and nanotubes by means of closed clusters. Section\[sec:Impurity\] contains the calculations of the graphene energy spectrum in the presence of impurity. Finally, in \[sec:monoatomic layer\] we study the energy band structure of the hypothetic monoatomic layer C$_{1-x}$ Si$_{x}$ $ \; (0\leq x \leq 1)$. Section\[sec:Con\] concludes with a discussion of the obtained results and furthermore describes a possibility for making the approach more precise as well as the application of the CC approach to other problems.

The essence of the CC approach and a rule for constructing the diagrams 