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Systematic tight-binding investigations of the electronic spectra (as afunction of the magnetic field) are presented for trigonal graphene nanoflakeswith reconstructed zigzag edges, where a succession of pentagons and heptagons,that is 5-7 defects, replaces the hexagons at the zigzag edge. For nanoflakeswith such reczag defective edges, emphasis is placed on topological aspects andconnections underlying the patterns dominating these spectra. The electronicspectra of trigonal graphene nanoflakes with reczag edge terminations exhibitcertain unique features, in addition to those that are well known to appear forgraphene dots with zigzag edge termination. These unique features includebreaking of the particle-hole symmetry, and they are associated with nonlineardispersion of the energy as a function of momentum, which may be interpreted asnonrelativistic behavior. The general topological features shared with thezigzag flakes include the appearance of energy gaps at zero and low magneticfields due to finite size, the formation of relativistic Landau levels at highmagnetic fields, and the presence between the Landau levels of edge states (thesocalled Halperin states) associated with the integer quantum Hall effect.Topological regimes, unique to the reczag nanoflakes, appear within a stripe ofnegative energies E_b < E < 0, and along a separate feature forming aconstant-energy line outside this stripe. The lower bound (E_b) specifying theenergy stripe is independent of size. A main finding concerns the limitedapplicability of the continuous Dirac-Weyl equation, since the latter does notreproduce the special reczag features. (See also the extended abstract in thepaper.)

Graphene flakes with defective edge terminations: Universal and topological aspects, and one-dimensional quantum behavior