When an all-benzenoid nanographene is linearly unzipped into oxygen-joined fragments, the oxidized benzenoid rings (aromatic sextets) selectively adopt the low-spin (DeltaS = 0) or high-spin conformation (DeltaS = 1) to yield the thermally most stable isomer. The selection of the conformation depends simply on the position of the aromatic sextets: the inner ones prefer the high-spin conformation, whereas the peripheral ones prefer the low-spin conformation. Therefore, the resulting most stable isomer has a total spin whose value equals the number of inner aromatic sextets (n(i)) along the oxidizing line. The nanographene fragments contained in this isomer have a ferromagnetic spin coupling. Due to the tautomerization between the high-spin and low-spin conformations, there also exist other possible isomers with higher energies and with spins at ground state ranging from 0 to (n(i) - 1). The rich geometrically correlated spins and the adjustable energy gaps indicate great potential of the graphene oxides in spintronic devices.