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Several quantities are calculated and discussed, such as the proton fraction and the direct Urca behavior, the density dependence of the speed of sound and the trace anomaly, the crust-core transition properties, the compatibility with astrophysical observations, and the neutron matter properties from chiral effective-field theory calculations and pQCD constraints.<\/jats:p>\n<jats:p><jats:italic>Methods.<\/jats:italic> We construct unified EOSs where the outer crust is given by the BSk22 functional and the inner crust is calculated from a compressible liquid drop approximation. The core is purely nucleonic; made of protons, neutrons, electrons, and muons; under charge neutrality; and in <jats:italic>\u03b2<\/jats:italic>-equilibrium conditions.<\/jats:p>\n<jats:p><jats:italic>Results.<\/jats:italic> The correlation of the slope of the symmetry energy at saturation with the crust-core transition density and proton fraction is analyzed, and equations that translate these relations are proposed. Moreover, the spectral representation for all the EOSs is given, which is a convenient representation to study quasi-periodic oscillations with realistic EOSs. We show that several of these EOSs have in the center of the most massive neutron star a speed of sound squared on the order of \u22720.5. Most of the EOSs predict a maximum central density on the order of about six times the nuclear saturation density. Three of the EOSs satisfy all of the constraints imposed. 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