  We analyze samples of nearby clusters taken from the Abell catalog and the
X-ray Sample of Bright Clusters(De Grandi et al 1999) including a wide range of
X-ray luminosities.Using the usually adopted background subtraction procedures,
we find that galaxies in clusters selected by means of their X-ray emission
show a flat luminosity function (faint end slope $\alpha \simeq -1.1$)
consistent with that derived for galaxies in the field and groups. By contrast,
the sample of Abell clusters that do not have an X-ray counterpart shows a
galaxy luminosity function with a steep faint end ($\alpha \simeq -1.6$). We
investigate the possibility that cD halos could be formed by the disruption of
galaxies in rich relaxed clusters that show an apparently flat faint end galaxy
luminosity function (Lopez-Cruz et al 1997).
  We find that clusters dominated by a central cD galaxy (Bautz-Morgan classes
I and II) show the same systematic trend: X-ray selected clusters have flatter
faint end slopes than those clusters with no detected X-ray emission. Thus, it
is likely the X-ray selection and not the cluster domination by central
galaxies what correlates with background decontamination estimates of the
galaxy luminosity function. Moreover, no significant correlation between X-ray
luminosity and the galaxy LF faint end slope is found. These results do not
support a scenario where flat faint end slopes are a consequence of cD
formation via the disruption of faint galaxies. We argue that the clusters
without X-ray emission are strongly affected by projection effects which give
rise to spurious faint end slopes estimated using background subtraction
procedures (Valotto et al 2001).
