  We investigate the star-formation properties of dynamically relaxed galaxy
clusters as a function of cluster mass for 308 low-redshift clusters drawn from
the Sloan Digital Sky Survey (SDSS) C4 cluster catalog. It is important to
establish if cluster star-formation properties have a mass dependence before
comparing clusters at different epochs, and here we use cluster velocity
dispersion as a measure of cluster mass. We find that the total stellar mass,
the number of star-forming galaxies, and total star-formation rate scale
linearly with the number of member galaxies, with no residual dependence on
cluster velocity dispersion. With the mass-dependence of cluster star-formation
rates established, we compare the SDSS clusters with a sample of z = 0.75
clusters from the literature and find that on average the total H-alpha
luminosity of the high-redshift clusters is 10 times greater than that of the
low-redshift clusters. This can be explained by a decline in the H-alpha
luminosities of individual cluster galaxies by a factor of up to 10 since z =
0.75. The magnitude of this evolution is comparable to that of field galaxies
over a similar redshift interval, and thus the effect of the cluster
environment on the evolution of star-forming galaxies is at most modest. Our
results suggest that the physical mechanism driving the evolution of cluster
star-formation rates is independent of cluster mass, at least for clusters with
velocity dispersion greater than 450 km/s, and operates over a fairly long
timescale such that the star-formation rates of individual galaxies decline by
an order of magnitude over ~7 billion years. (Abridged)
