A fundamental relation exists between supermassive black holes (BHs) and their host galaxies, with BH masses closely correlated to the velocity dispersions of their host bulges, $ M_{\bullet} \propto \sigma^{\alpha} $, where $ \alpha = 4.8 \pm 0.5 $. This correlation is much tighter than the relation between BH masses and bulge luminosity, with minimal intrinsic scatter. BH masses estimated by Magorrian et al. (1998) lie systematically above the $ M_{\bullet} - \sigma $ relation defined by more accurate mass estimates, some by as much as two orders of magnitude. The tightness of the $ M_{\bullet} - \sigma $ relation suggests a strong link between BH formation and the properties of the stellar bulge. The study investigates the connection between BH masses and the stellar velocity dispersion of the host galaxy. Using galaxies with well-determined BH masses, a remarkably tight correlation is found with negligible intrinsic scatter. This suggests that the stellar velocity dispersion may be the fundamental parameter regulating the evolution of supermassive BHs in galaxies. The database includes secure BH mass estimates and properties of the host galaxies. Distances are derived from surface brightness fluctuation (SBF) data, and velocity dispersions are measured with a consistent definition. The analysis shows that the correlation between BH masses and bulge magnitude $ B_{T}^{0} $ is poor, while the correlation with central velocity dispersion $ \sigma_{c} $ is remarkable. The best-fit linear relation is $ \log M_{\bullet} = 4.80(\pm0.54)\log\sigma_{c} - 2.9(\pm1.3) $, with a reduced $ \chi^{2} $ of 0.8, consistent with a scatter due to measurement errors. Sample A, with the most accurate BH mass estimates, defines a tight linear relation between $ M_{\bullet} $ and $ \sigma_{c} $, while Sample B, with less reliable estimates, shows a weaker correlation. The difference is attributed to the reliability of the BH mass estimates and the method used to derive them. The study concludes that the $ M_{\bullet} - \sigma $ relation is a fundamental link between BHs and their host galaxies, with BH masses being closely regulated by the velocity dispersion of the stellar bulge.A fundamental relation exists between supermassive black holes (BHs) and their host galaxies, with BH masses closely correlated to the velocity dispersions of their host bulges, $ M_{\bullet} \propto \sigma^{\alpha} $, where $ \alpha = 4.8 \pm 0.5 $. This correlation is much tighter than the relation between BH masses and bulge luminosity, with minimal intrinsic scatter. BH masses estimated by Magorrian et al. (1998) lie systematically above the $ M_{\bullet} - \sigma $ relation defined by more accurate mass estimates, some by as much as two orders of magnitude. The tightness of the $ M_{\bullet} - \sigma $ relation suggests a strong link between BH formation and the properties of the stellar bulge. The study investigates the connection between BH masses and the stellar velocity dispersion of the host galaxy. Using galaxies with well-determined BH masses, a remarkably tight correlation is found with negligible intrinsic scatter. This suggests that the stellar velocity dispersion may be the fundamental parameter regulating the evolution of supermassive BHs in galaxies. The database includes secure BH mass estimates and properties of the host galaxies. Distances are derived from surface brightness fluctuation (SBF) data, and velocity dispersions are measured with a consistent definition. The analysis shows that the correlation between BH masses and bulge magnitude $ B_{T}^{0} $ is poor, while the correlation with central velocity dispersion $ \sigma_{c} $ is remarkable. The best-fit linear relation is $ \log M_{\bullet} = 4.80(\pm0.54)\log\sigma_{c} - 2.9(\pm1.3) $, with a reduced $ \chi^{2} $ of 0.8, consistent with a scatter due to measurement errors. Sample A, with the most accurate BH mass estimates, defines a tight linear relation between $ M_{\bullet} $ and $ \sigma_{c} $, while Sample B, with less reliable estimates, shows a weaker correlation. The difference is attributed to the reliability of the BH mass estimates and the method used to derive them. The study concludes that the $ M_{\bullet} - \sigma $ relation is a fundamental link between BHs and their host galaxies, with BH masses being closely regulated by the velocity dispersion of the stellar bulge.