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