Polycyclic aromatic hydrocarbons exhibit a rich spectrum of physicochemical properties depending on the size and, more critically, on the edge and bond topologies. Among them, open-shell systems - molecules hosting unpaired electron densities - represent an important class of materials for organic electronic, spintronic, and optoelectronic devices, but remain challenging to synthesize in solution. We report the on-surface synthesis and scanning tunneling microscopy- and spectroscopybased study of two ultralow-gap open-shell molecules, namely peri-tetracene, a benzenoid graphene fragment with zigzag edge topology, and dibenzo[a,m]dicyclohepta-[bcde,nopq]rubicene, a nonbenzenoid nonalternant structural isomer of peri-tetracene with two embedded azulene units. Our results provide an understanding of the ramifications of altered bond topologies at the single-molecule scale, with the prospect of designing functionalities in carbon-based nanostructures via engineering of bond topology.