The current study uses the relativistic mean field approach to investigate the nuclear structure of selected even-even neutron-rich nuclei spanning from the stability line to the neutron drip line. Specifically, the nuclei studied include ^16–28O, ^30–42Si, ^48–60Ca, ^56–68Ni, ^88–100Kr, ^96–122Ru, ^140–152Ba, ^142–154Sm, and ^150–162Er. The relativistic Hartree-Bogoliubov (RHB) method was applied, incorporating effective density-dependent point coupling (DD-PC) and density-dependent meson exchange (DD-ME) interactions. The impact of these interactions was demonstrated through the calculation of various nuclear structure properties, including binding energy (BE), kinetic energy (KE), pairing energy (PE), root mean square (rms) charge radius, two-neutron separation energy (S_2n), mass densities (ρ_m), and triaxial deformation. The calculated results were compared with the available experimental data. It is clear that the RMF approach, particularly with the DD-ME2 and DD-PC1 effective interactions, proved to be a valuable tool for studying nuclear properties near the drip lines and away from stability, providing insights into the behavior of exotic or halo nuclei.