We demonstrate the relationship between the topology (the way in which the atoms are connected), open-shell character, and singlet fission (SF) propensity in a series of diboron-doped anthracenes and phenanthrenes. The study is performed by using high-level wave-function-based quantum-chemical calculations. The results show that the molecular topology plays a crucial role for the optical properties and, respectively, for the SF propensity of the studied compounds. The topology-derived correlations between the structure and properties are interpreted in the light of the Kekulé hydrocarbons concept and serve as molecular design guidelines for the discovery of new SF materials. Finally, several boron-doped polycyclic aromatic hydrocarbons are proposed as SF chromophores for organic solar cells.