  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 transformation 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.
