, defining the three known categories of AGNRs, which are basically categorized in terms of their aromaticity patterns and the symmetry of frontier MOs, which are intimately interconnected. On the basis of eq. ( ) thin AGNRs are defined those with n=1, i.e. Z=3, 4, 2, or W=7, 9, 5, whereas wider AGNRs are characterized by n≥2. Concerning topological end-states in wider AGNRs, it has been illustrated recently that the number of pairs (occupied-unoccupied) of end-states is equal to n. Therefore, wider AGNRs are characterized by n≥2 pairs of topological end-states of opposite parities and nearly equal energies which facilitates CQI, as is illustrated in Fig. , for the 13-AGNRs (n=2, Z=7, W=13). As we can see in Fig. , CQI is manifested by an abrupt increase in conductivity by a factor of about 2.5. At the same critical length, the HOMO-LUMO as well as the (HOMO-1)-(LUM+1) gaps begin to suddenly rise approaching each other up to the length ~80 Å where they practically coincide and the CQI region ends. Chen et al. analysing the measured central peak at 1.4 eV of 13-AGNRs (n=2, Z=6) concluded that in fact it consists of two separate peaks with an energy separation of 0.11eV between them and extending up to 30 Å along the (longitudinal) axis of the AGNR. AGNRs, before and after the "phase transition" respectively. Similar comparisons for the frontier MOs of the 6x6 and 6x12 AGNRs is given in (b).