Absolute Magnitude Calibration for Red Giants based on the
  Colour-Magnitude Diagrams of Galactic Clusters. I- Calibration with V and
  (B-V)
  We present an absolute magnitude calibration for red giants with the colour
magnitude diagrams of six Galactic clusters with different metallicities i.e.
M92, M13, M5, 47 Tuc, M67, and NGC 6791. The combination of the absolute
magnitude offset from the fiducial of giant sequence of the cluster M5 with the
corresponding metallicity offset provides calibration for absolute magnitude
estimation for red giants for a given (B-V)o colour. The calibration is defined
in the colour interval 0.75<=(B-V)o<=1.50 mag and it covers the metallicity
interval -2.15<[Fe/H]<=+0.37 dex. 91% of the absolute magnitude residuals
obtained by the application of the procedure to another set of Galactic
clusters lie in the interval -0.40<\Delta M<=+0.40 mag. The mean and the
standard deviation of the residuals are 0.05 and 0.19 mag, respectively. We
fitted the absolute magnitude also to metallicity and age for a limited
sub-sample of (B-V)o colour, just to test the effect of age in absolute
magnitude calibration. Comparison of the mean and the standard deviation of the
residuals evaluated by this procedure with the corresponding ones provided by
the procedure where the absolute magnitude fitted to a third degree polynomial
of metallicity show that the age parameter may be omitted in absolute magnitude
estimation of red giants. The derived relations are applicable to stars older
than 4 Gyr, the age of the youngest calibrating cluster.
