  The relativistic mean-field models tested in previous works against nuclear
matter experimental values, critical parameters and macroscopic stellar
properties are revisited and used in the evaluation of the symmetry energy
$\gamma$ parameter obtained in three different ways. We have checked that
independent of the choice made to calculate the $\gamma$ values, a trend of
linear correlation is observed between $\gamma$ and the symmetry energy
($\mathcal{S}_0$) and a more clear linear relationship is established between
$\gamma$ and the slope of the symmetry energy ($L_0$). These results directly
contribute to the arising of other linear correlations between $\gamma$ and the
neutron star radii of $R_{1.0}$ and $R_{1.4}$, in agreement with recent
findings. Finally, we have found that short-range correlations induce two
specific parametrizations, namely, IU-FSU and DD-ME$\delta$,
simultaneouslycompatible with the neutron star mass constraint of $1.93 <
M_{max}/M_\odot < 2.05$ and with the overlap band for the
$L_0\times\mathcal{S}_0$ region, to present $\gamma$ in the range of
$\gamma=0.25\pm0.05$.
