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The Adam-Gibbs (AG) relation connects the dynamics of a glass-forming liquid to its thermodynamics via the configurational entropy and is of fundamental importance in descriptions of glassy behavior. The breakdown of the Stokes-Einstein relation (SEB) between the diffusion coefficient and the viscosity (or structural relaxation times) in glass formers raises the question as to which dynamical quantity the AG relation describes. By performing molecular dynamics simulations, we show that the AG relation is valid over the widest temperature range for the diffusion coefficient and not for the viscosity or relaxation times. Studying relaxation times defined at a given wavelength, we find that SEB and the deviation from the AG relation occur below a temperature at which the correlation length of dynamical heterogeneity equals the wavelength probed.