Abstract
In this study we found the existence of the FP for a final sample of 24 galaxy clusters, where sampling and signal to noise of the data allows a reliable analysis. For this purpose, we have introduced a new formalism for measure size and velocity dispersion. We found that indeed the parameter space of galaxy clusters accepts a FP (CFP) R ∝ σ^{1.19± 0.12} I^{-8.18±0.44}, proved the hypothesis of virialized central regions in clusters of galaxies. To do a more autoconsistent analysis we obtain the FP of galaxy clusters and found similarity to the CFP, given important consequences, showing that the mass-luminosity ratio should have the same functional form for the cluster galaxies and galaxy clusters. We showed that in fact the mass-luminosity ratio of clusters of galaxies (M/L ∝ L^{0.54±0.22}) follows the same scaling law of elliptical galaxies. This result imposes a strong constraint to galaxies formation models.
