  In this paper we investigate the electron-phonon coupling in bilayer
graphene, as a paradigmatic case for multilayer graphenes where interlayer
hoppings are relevant. Using a frozen-phonon approach within the context of
Density Functional Theory (DFT) and using different optical phonon
displacements we are able to evaluate quantitatively the electron-phonon
coupling $\alpha_i$ associated with each hopping term $\gamma_i$. This analysis
also reveals a simple scaling law between the hopping terms $\gamma_i$ and the
electron-phonon coupling $\alpha_i$ which goes beyond the specific DFT
technique employed.
