Obviously, the same molecules can be used as models for the corresponding finite (thin) zigzag nanoribbons (ZGNRs). It has been suggested and verified here that anti-aromaticity (of the non-hexagonal rings) is the driving force for open-shell electronic states in the non-alternant isomers of peri-acenes. This could be contrasted with the aromaticity and closed-shell states of alternant AGNRs (and peri-acenes), which is the key factor for their electronic properties. Thus, one would expect that the alternant isomers, peri-acenes themselves (with only hexagonal rings), would be naturally closed shell electronic states. We show here, contrary to opposite reports, that the alternat peri-acenes have indeed closed shell ground states with no . A.D. Zdetsis "Open-shell states in alternant and non-alternant Nanographenes" 4 conventional magnetism. This has been recently illustrated for all (alternant) atomically precise AGNRs, which have finite length. Such atomically precise AGNRs have been lately synthesized by bottom-up technics using molecular precursors (on metallic, and recently non-metalic substrates) which at the initial stages consist of various peri-acenes, such as bisanthene, peri-tetracene, etc. The electronic (band gaps, spin-states, symmetry) and topological characteristics of such AGNRs have been recently rationalized and reconciled by the present author and collaborators (among others). The AGNRs with Z zigzag rings in their ends and A armchair rings in their edges have been denoted as ZxA. We have shown, contrary to established beliefs, that the ground state of such (alternant) AGNRs, including in the limit of "short" AGNRs the "parent" peri-acenes (A=2), is a closed singlet. For benzenoid systems open shell states of usually high spin occur in cases of considerable sublattice imbalance as in triangulenes and related structures (Clar's goblet, etc). The focus here is in AGNRs, and in particular AGNRs with A=2, such as bisanthene and peritetracene (3x2, 4x2) and their non alternat isomers SW3x2 and SW4x2 AGNRs (and peri-acenes), similarly (or contrary) to the anti-aromaticity of their nonalternant isomers. We show that one fundamental difference between alternant and nonalternant isomers is the breaking of the electron-hole symmetry in the latter. Thus, alternant topology can be recognized as the root of electron hole symmetry. Lack of such symmetry in non-alternant NGRs and GNRs can lead to distorted Dirac points (cones) around the Fermi level with end/edge localized higher occupied molecular orbitals (HOMO), but non-localized lowest unoccupied molecular orbitals (LUMO). This could have important technological and scientific implications and applications, which however are beyond the scope of the present work. In what follows, after the description of the theoretical and computational details in section 2, section 3 is devoted in the detailed description of the alternant "molecules" of bisanthene and perytetracene, whereas their non-alternant isomers are described in section 4. Finally, the conclusions of the present work are summarized in section 5.