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 (R_e), absolute magnitude and central velocity dispersion (σ₀)) and their host groups and clusters velocity dispersion (σ_cl). This type of relations suggests that the most massive groups or clusters host larger central galaxies. On the other hand, the σ₀/σ_cl ratio as a function of σ_cl is consistent with [10].