Using the inherent shell structure of graphene and geometrical/topological constrains, we verify that there are only three families of armchair graphene nanoribbons (AGNR) with Z zigzag edge-rings, categorized by Z=3n, 3n±1, n=1,2,… each with unique aromatic, electronic and topological properties. The Z=3n+1, 3n AGNR-families are aromatic with large bandgaps,characteristic aromaticity-patterns, and unique “active” frontier orbitals, in contrast to the ordinary ones. Such AGNRs due to sublattice/molecular-group symmetry-conflict develop 2n zigzag-edge-localized “gapless” frontier-states, which are “pseudospin-polarized” (not real-spin-polarized) with total pseudospin S=n, effectively optimizing sublattice “balance” and total energy. The “active” frontier orbitals, obtained after neglecting such gapless non-bonding states, have large “active” bandgaps, which are in very good agreement with experiment. The Z=3n-1 AGNRs have mixt aromatic, electronic and topological character, with vanishingly small bandgaps. Zigzag GNRs, contrary to opposite reports, have no magnetic zigzag edges, unless magnetization due to polarization of atomic pz orbital angular momentum is operative<br>
Analytical and semianalytical tools to determine the topological character of Shiba chains