  An exact description of $\pi$ electrons based on the tight-binding model of
graphene as an alternant, plane macromolecule is presented. The model molecule
can contain an arbitrary number of benzene rings and has armchair- and
zigzag-shaped edges. This suggests an instructive alternative to the most
commonly used approach, where the reference is made to the honeycomb lattice
periodic in its A and B sublattices. Several advantages of the macromolecule
model are demonstrated. The newly derived analytical relations detail our
understanding of $\pi$ electron nature in achiral graphene ribbons and carbon
tubes and classify these structures as quantum wires.

Mesoscale and Nanoscale Physics;Materials Science