By analyzing Chandra X-ray data of a sample of 21 galaxy groups and 19galaxy clusters,we find that in 31 sample systems there exists a significant central(R ≤10h-171 kpc)gas entropy excess(△K0),which corresponds to(=)0.1-0.5 keV per gas particle,beyond the power-law model that best fits the radial entropy profile of the outer regions.We also find a distinct correlation between the central entropy excess△K0 and K-band luminosity LK of the central dominating galaxies(CDGs),which is scaled as △K0 ∝ L1.6±0.4K,where LK is tightly associated with the mass of the supermassive black hole hosted in the CDG.In fact,if an effective mass-to-energy conversion-efficiency of 0.02 is assumed for the accretion process,the cumulative AGN feedback EAGNfeedback(=)ηMBHC2 yields an extra heating of(=)0.5-17.0keV per particle,which feedback is sufficient to explain the central entropy excess.In most cases,the AGN contribution can compensate the radiative loss of the X-ray gas within the cooling radius((=)0.002-2.2 keV per particle),and apparently exceeds the energy required to cause the scaling relations to deviate from the self-similar predictions((=)0.2-1.0 keV per particle).In contrast to the AGN feedback,the extra heating provided by supernova explosions accounts for(=)0.01-0.08 keV per particle in groups and is almost negligible in clusters.Therefore,the observed correlation between ΔK0 and LK can be considered as direct evidence for AGN feedback in galaxy groups and clusters.