The initial relaxation dynamics of the photoexcited fullerenes C60, C70, C76, C84, C86, and C90 were investigated by dispersion-free femtosecond pump-probe spectroscopy. Under identical excitation conditions, the formation of the lowest excited state slows down for the larger fullerenes. This trend in dynamics, monitored throughout the visible and NIR range, is found to correlate with the number of isomers in accordance with the isomerization mechanism suggested by Stone and Wales. The Stone-Wales isomerization was calculated as thermally inaccessible but photoinduced barrierless. The energy difference of the isomers is in the 1 meV range, and back-isomerization is observed on the picosecond time scale. The characteristic spectrally broad transient absorption of the investigated fullerenes is promising for fast optical gating applications.