A study of the luminosity function of 36 Abell clusters of galaxies has been carried out using photographic plates obtained with the Palomar 1.2 m Schmidt telescope. The relation between the magnitude M_1 of the brightest cluster member and the Schechter function parameter M* has been analyzed. A positive correlation between M* and M_1 is found. However clusters appear segregated in the M_1-M* plane according to their Rood & Sastry class in such a way that on average M_1 becomes brighter while M* becomes fainter going from late to early Rood & Sastry and also Bautz & Morgan classes. Also a partial correlation analysis involving the magnitude M_10 of the 10th brightest galaxy, shows a negative intrinsic correlation between M_1 and M*. These results agree with the cannibalism model for the formation of brightest cluster members, and provide new constraints for theories of cluster formation and evolution.
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