The low-energy essential properties of the π-electronic states on graphene-related nanotubes [1] and nanoribbons [2]. Using the single-orbital tight-binding functions [3], the various Hamiltonian matrices could be built for the geometry-enriched single-walled/mono-layer systems. Evaluate the independent matrix elements, only with the nearest-neighbor interactions, in (a) armchair and (b) zigzag carbon nanotubes and (c) armchair and (d) zigzag graphene nanoribbons. (e)/(f)/(g)/(h) Clearly illustrate the main features of electronic energy spectra. It should be noticed that certain electronic states show unique probability distributions. Finally, (i) explore the 1D van Hove singularities and the important differences between these two systems.