0_5501 Polycyclic aromatic hydrocarbons (PAHs), occasionally called molecular graphenes, are finite, conjugated portions of graphene. PAHs are potential light-harvesting materials for organic solar cells because their bandgap is relatively low and highly depends on their molecular structure. Controlling the bandgap of PAHs based on molecular structure considerations would thus be crucial. At the current level of understanding, the bandgap of a PAH decreases with an increase in conjugation, which in turn depends on the number of condensed aromatic rings contained in the molecule and on the level of delocalization of its π electrons. A relationship should thus exist between the bandgap of a PAH and the disposition of its benzenoid rings; such a relationship, however, is expected to be complicated and is still unknown. We here adopt a graph-theoretical approach to investigate the relationship between the bandgap and the ring disposition of PAHs. In particular, we reduce each of several PAHs to a colored subgraph of the infinite dualist graph of graphene: here a vertex v_i exists for each benzenoid ring, and the edge e_ij exists if the i-th and j-th rings are condensed. The colored subgraph unifies the description of the backbone and the border of a PAH, and its graph invariants contain structural information. We then try to relate the energy difference of the Kohn-Sham frontier molecular orbitals to a function of simple dualist-graph invariants.