remain in each case, namely those of the coefficients $c_2$ and $c_3$, and consequently only two values of energy for each $A_x S_y$ and $A_x A_y$.

The energy levels for various symmetries are shown in Tab.\[table2\], Tab.\[table3\] shows the values of the coefficients $c_1, c_2, \ldots, c_{12}$. These coefficient values are obtained by solving the system of equations like and analogous systems for other symmetries for the energies $\varepsilon = 0. \pm 1, \pm 3$. The set of these coefficients determines the wave functions for various symmetries within our considered model. Tab.\[table2\] and \[table3\] also show the Brillouin zone symmetry points, which can also be seen in Fig.\[Fig3\].

For the purpose of illustration one can represent these functions graphically by extending the cluster over the whole graphene layer. In the case $\varepsilon = \pm 1$ the functions coincide with those in [@Wallace]. For the case $\varepsilon = 0$, wave functions for various symmetries are shown in Fig.\[Fig6\].

[&gt;m[3.5 cm]{}|&gt;m[1.0 cm]{}&gt;m[1.0 cm]{}&gt;m[1.0 cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}&gt;m[1.0cm]{}]{} & $\varepsilon_1$ & $\varepsilon_2$ & $\varepsilon_3$ & $\varepsilon_4$ & $\varepsilon_5$ & $\varepsilon_6$ & $\varepsilon_7$ & $\varepsilon_8$ & $\varepsilon_9$ & $\varepsilon_{10}$ & $\varepsilon_{11}$ & $\varepsilon_{12}$\
$S_x S_y$ & & & & & & & & & & & &\
