for the symmetric nucleus $^{100}$Sn, it is interesting to see that the dependence of $E_{ave}$ on the isospin relevant macroscopic quantities, namely, $L$, $G_{V}$, $E_{\text{\textrm{sym}}}(\rho _{0})$, $m_{v,0}^{\ast }$ is very weak. We have also checked the case of the stable nucleus $^{90}$Zr for the correlation analysis as in Fig. \[XEcSn100132\], and we find the results are very similar to the case of $^{100}$Sn, namely, displaying a much weak correlation with the $L$ parameter while a stronger correlation with the $G_{S}$ parameter compared with the case of $^{208}$Pb. This may be understandable from the fact that the $^{90}$Zr has a smaller isospin asymmetry, i.e., $(N-Z)/A=0.11$ compared with $^{208}$Pb where we have ($N-Z)/A=0.21$. In addition, the surface coefficient $G_{S}$ may become more important for lighter nuclei as expected, leading to a stronger correlation with the $G_{S}$ parameter. From these results, it seems that the ISGMR of a heavier and more symmetric nucleus, where the symmetry energy effects will be reduced significantly, may be more suitable for extracting the $K_{0}$ parameter. In addition, the different $E_{ave}$-$m_{s,0}^{\ast }$ correlations between $^{100}$Sn and $^{132}$Sn observed in Fig. \[XEcSn100132\] can be understood from the fact that $K_{\mathrm{sat,2}}$ parameter decreases with $m_{s,0}^{\ast }$ as shown in Fig. 