This study explores the sensitivity of the equation of state (EoS) of dense asymmetric nuclear matter on the nuclear matter incompressibility $K$ and assesses the corresponding effects on the structural properties of neutron stars. To isolate the effect of $K$, we employ six relativistic mean-field parameter sets in which $K$ is systematically varied over the range 200–300 MeV, while the slope of symmetry energy is constrained to a fixed value, ensuring that the observed variations arise primarily from incompressibility. The resulting parameter sets are calibrated to reproduce ground-state properties of finite nuclei and bulk properties of symmetric nuclear matter. The corresponding EoSs for $\beta$-stable matter are then employed to evaluate several neutron-star properties. We find that $K$ affects the stiffness of the EoS at suprasaturation densities, primarily through modifications in higher-order density derivatives such as the skewness parameter $Q_0$. Larger values of $K$ lead to a stiffer EoS, resulting in systematically larger radii and tidal deformabilities, while the maximum mass shows comparatively weaker sensitivity. The radius $R_{1.4}$ of a canonical $1.4M_{\odot }$ neutron star and its associated dimensionless tidal deformability ${\mathrm{\Lambda }}_{1.4}$ respond sensitively to changes in the incompressibility parameter. The neutron-star properties lie in the ranges $M_{max}\approx 2.01M_{\odot }\text{–}2.18M_{\odot }, R_{1.4}\approx 12.88\text{–}13.30\mathrm{km}$, and ${\mathrm{\Lambda }}_{1.4}\approx 550.01\text{–}695.62$, consistent with observational constraints from NICER measurements and gravitational-wave events such as GW170817 and GW190814. The softer EoSs corresponding to lower $K$ values show better agreement with recent bounds on tidal deformability. The present study demonstrates that nuclear incompressibility plays an important role in governing the high-density behavior of the EoS and the structural properties of neutron stars, providing a clearer connection between terrestrial nuclear matter constraints and astrophysical observations of compact stars.

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• Equations of state of nuclear matter
• Nuclear astrophysics
• Nuclear matter in neutron stars
• Symmetry energy