A unified equation of state (EOS) for dense neutron star matter is calculated using the SLy effective nuclear interaction. This EOS describes both the neutron star crust and the liquid core. The crust is modeled using the Compressible Liquid Drop Model (CLDM), while the liquid core is calculated assuming a minimal npe μ composition. The crust-core transition is a weak first-order phase transition with a small density jump. The EOS of the liquid core is determined using the SLy interaction, and parameters of static neutron stars are calculated and compared with observational data. The minimum and maximum masses of static neutron stars are found to be 0.094 M☉ and 2.05 M☉, respectively. The effects of rotation on these masses are briefly discussed. The SLy EOS is found to be particularly suitable for neutron star interior calculations due to its emphasis on neutron-excess dependence. The EOS is validated against experimental data and is shown to reproduce ground state energies of doubly magic nuclei. The unified EOS is used to calculate neutron star models, which are compared with those based on the FPS interaction. The results show that neutron star models based on the unified EOS are not significantly different from those using the FPS interaction. The EOS is also used to calculate the adiabatic index, which is found to vary with density and composition. The sound speed is calculated and found to be subluminal for all stable neutron star models. The gravitational mass versus central density curve is shown, with the maximum mass at 2.05 M☉. The radius of neutron stars is found to decrease slightly with increasing mass, and the surface redshift is calculated for different masses. The results are compared with observational data and other EOS models. The study highlights the importance of the EOS in understanding neutron star structure and properties.A unified equation of state (EOS) for dense neutron star matter is calculated using the SLy effective nuclear interaction. This EOS describes both the neutron star crust and the liquid core. The crust is modeled using the Compressible Liquid Drop Model (CLDM), while the liquid core is calculated assuming a minimal npe μ composition. The crust-core transition is a weak first-order phase transition with a small density jump. The EOS of the liquid core is determined using the SLy interaction, and parameters of static neutron stars are calculated and compared with observational data. The minimum and maximum masses of static neutron stars are found to be 0.094 M☉ and 2.05 M☉, respectively. The effects of rotation on these masses are briefly discussed. The SLy EOS is found to be particularly suitable for neutron star interior calculations due to its emphasis on neutron-excess dependence. The EOS is validated against experimental data and is shown to reproduce ground state energies of doubly magic nuclei. The unified EOS is used to calculate neutron star models, which are compared with those based on the FPS interaction. The results show that neutron star models based on the unified EOS are not significantly different from those using the FPS interaction. The EOS is also used to calculate the adiabatic index, which is found to vary with density and composition. The sound speed is calculated and found to be subluminal for all stable neutron star models. The gravitational mass versus central density curve is shown, with the maximum mass at 2.05 M☉. The radius of neutron stars is found to decrease slightly with increasing mass, and the surface redshift is calculated for different masses. The results are compared with observational data and other EOS models. The study highlights the importance of the EOS in understanding neutron star structure and properties.