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Based on the distribution of tidal deformabilities and component masses of binary neutron star merger GW170817, the parametric equation of states (EOS) are employed to probe the nuclear symmetry energy and the properties of neutron star. To obtain a proper distribution of the parameters of the EOS that is consistent with the observation, Bayesian analysis is used and the constraints of causality and maximum mass are considered. From this analysis, it is found that the symmetry energy at twice the saturation density of nuclear matter can be constrained within $E_{sym}(2{\rho_{0}})$ = $34.5^{+20.5}_{-2.3}$ MeV at 90\% credible level. Moreover, the constraints on the radii and dimensionless tidal deformabilities of canonical neutron stars are also demonstrated through this analysis, and the corresponding constraints are 10.80 km $< R_{1.4} <$ 13.20 km and $133 < \Lambda_{1.4} < 686$ at 90\% credible level, with the most probable value of $\bar{R}_{1.4}$ = 12.60 km and $\bar{\Lambda}_{1.4}$ = 500, respectively. With respect to the prior, our result (posterior result) prefers a softer EOS, corresponding to a lower expected value of symmetry energy, a smaller radius and a smaller tidal deformability., Comment: 15 pages, 15 figures

Similar to the compactness parameter ($\beta=M/R$), the gravitational binding energy (GBE) is also a characteristic parameter which can reflect the internal structure of a neutron star and thus can be used to expressing the universal relations. Scaling by the stellar mass, this investigation demonstrates a perfect universal relation between the GBE and the moment of inertia, where both of the normal neutron stars and the quark stars satisfy the same universal relation. Moreover, a fine empirical relation between the GBE and the tidal deformability is proposed, where the difference of the relations can be used to distinguish wether a pulsar is a normal neutron star or a quark star if the stellar mass and the tidal deformability can be observed or estimated rather accurately. These universal relations provide a potential way to estimate the GBE if the stellar mass and the moment of inertia/the tidal deformability are precisely measured., Comment: 15 pages, 7 figures

Similar to the compactness parameter ($\beta=M/R$), the gravitational binding energy (GBE) is also a characteristic parameter which can reflect the internal structure of a neutron star and thus can be used to expressing the universal relations. Scaling by the stellar mass, this investigation demonstrates a perfect universal relation between the GBE and the moment of inertia, where both of the normal neutron stars and the quark stars satisfy the same universal relation. Moreover, a fine empirical relation between the GBE and the tidal deformability is proposed, where the difference of the relations can be used to distinguish wether a pulsar is a normal neutron star or a quark star if the stellar mass and the tidal deformability can be observed or estimated rather accurately. These universal relations provide a potential way to estimate the GBE if the stellar mass and the moment of inertia/the tidal deformability are precisely measured., Comment: 15 pages, 7 figures