We investigate relations between the color and luminosity distributions of cluster galaxies and the evolutionary state of their host clusters. Our aim is to explore some aspects of cluster galaxy evolution and the dynamical state of clusters as two sides of the same process. We used 10,721 member galaxies of 183 clusters extracted from the Sloan Digital Sky Survey using a list of NoSOCS and CIRS targets. First, we classified the clusters into two categories, Gaussian and non-Gaussian, according

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... to their velocity distribution measurements, which we used as an indicator of their dynamical state. We then used objective criteria to split up galaxies according to their luminosities, colors, and photometric mean stellar age. This information was then used to evaluate how galaxies evolve in their host clusters. Meaningful color gradients, i.e., the fraction of red galaxies as a function of radius from the center, are observed for both the Gaussian velocity distribution and the non-Gaussian velocity distribution cluster subsamples, which suggests that member galaxy colors change on a shorter timescale than the time needed for the cluster to reach dynamical equilibrium. We also found that larger portions of fainter red galaxies are found, on average, in smaller radii. The luminosity function in Gaussian clusters has a brighter characteristic absolute magnitude and a steeper faint-end slope than it does in the non-Gaussian velocity distribution clusters. Our findings suggest that cluster galaxies experience intense color evolution before virialization, while the formation of faint galaxies through dynamical interactions probably takes place on a longer timescale, possibly longer than the virialization time.