  The NMSSM provides an excellent dark matter candidate, usually, the lightest
neutralino ($\tilde{\chi}^0_1$) being the lightest supersymmetric particle
(LSP), in the universe. It is a mixture of the bino, the neutral wino, the
neutral higgsinos, and the singlino. In this work, we investigate the features
of the lightest neutralino by concentrating on a specific region of the NMSSM
parameter space with small values of both $\lambda$ and $\kappa$, taking into
account theoretical and experimental constraints, including relic density,
direct and indirect detection constraints. We have found that the LSP dark
matter is a singlino-dominated neutralino for most of the sample points of the
chosen scenario. Thus, contrary to expectations, the NMSSM is not comparable to
the MSSM in terms of dark matter properties as $\lambda$ and $\kappa$ are very
small. The LSP can also be either higgsino-dominated or bino-dominated in some
parameter space. The most important parameters affecting the mass and
properties of the LSP are $\kappa$, $\lambda/\kappa$, and $\mu_{\rm eff}$.
Further, we notice that $\sigma^{SI}_p \approx 1.02$ $\sigma^{SI}_n$ and
$\sigma^{SD}_p \approx 0.76$ $\sigma^{SD}_n$ for all the surviving sample
points.
