In this work we study the Double Exchange-Holstein (DE-H) model with an electron-phonon interaction $gamma$ coupled to magnetism. The analysis is performed combining a mean-field approximation for the double exchange interaction and the Lang-Firsov t
ransformation for the electron-phonon interaction. Discontinuous magnetic transitions appear when the dependence of $g$ with $m$ is sufficiently large, resembling those experimentally observed in manganites. We observe that the characteristic resistivity peak that arises near the critical temperature appears for broad ranges of the system parameter values, unlike what occurs in a constant--$gamma$ model.
