The ablation dynamics and cluster formation of $C_n^+$ ions ejected from 355 nm laser ablation of a graphite target in vacuum are investigated using a reflectron time-of-flight (RTOF) mass spectrometer. At low laser fluence, odd-numbered cluster ions with $3{leq}n{leq}15$ are predominantly produced. Increasing the laser fluence shifts the maximum size distribution towards small cluster ions, implying the fragmentation of larger clusters within the hot plume. The temporal evolution of $C_n^+$ ions was measured by varying the delay time of the ion extraction pulse with respect to the laser irradiation, providing significant information on the characteristics of the ablated plume. Above a laser fluence of $0.2J/cm^2$ , large cluster ions ($n{geq}30$) are produced at relatively long delay times, indicating that atoms or small carbon clusters aggregate during plume propagation. The dependence of the intensity of ablated $C_n^+$ ions on delay time after laser irradiation shows that the most probable velocity of each cluster ion decreases with cluster size.