the interaction between 1 and 1’ in 1(c), latter of which is absent in cluster $N=6$.

It must be noted, that for the numbers of atoms in sublattices A and B it is necessary to be equal, as closing bonds is only possible between atoms of different sublattices. For example, in cluster 1(b) it is only possible to close the bonds of atom 1 with atom 4, but not with 3 or 5. This restriction is necessary to satisfy Rule 1.

We also note that energy values obtained from the solution of secular equations are independent from the choice of the cluster in case of an “infinite” ideal lattice, but are only dependent from the number N. They are as well independent from the numeration of the atoms, since changes in numeration only cause determinant permutations.

Fig.\[Fig2\] shows some of the possible clusters with $N=12$ with dissimilar ways of closing.

To conclude this section, we note, that the name “closed cluster” which we use is different from the term “closed walk” used in graph theory [@Trinajstic]. For example, the cluster shown in Fig.\[Fig1a\] is a “closed walk”, but not a closed cluster - the latter is shown in Fig.\[Fig1b\].

One 