The data contained in this record, raw data of images and input files to reproduce calculations, support our recent report for the on-surface synthesis and characterization 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