Possible Relations between Brightest Central Galaxies and Their Host Galaxies Clusters and Groups

The r-band of the Sloan Digital Sky Survey (SDSS) for 17,924 brightest cluster galaxies (BCGs) in clusters and groups within 0.02 z 0.20 are used to study possible environmental relations affecting the nature of these galaxies. We find a correlation between BCGs physical properties (the effective radius (Re ), absolute magnitude and central velocity dispersion ({\sigma}0 )) and their host groups and clusters velocity dispersion ({\sigma}cl ). This type of relations suggests that the most massive groups or clusters host larger central galaxies. On the other hand, the {\sigma}0 /{\sigma}cl ratio as a function of {\sigma}cl is consistent with [10].