  While the equation of state (EOS) of symmetric nuclear matter (SNM) at
suprasaturation densities has been relatively well constrained from heavy-ion
collisions, the EOS of high-density neutron-rich matter is still largely
uncertain due to the poorly known high-density behavior of the symmetry energy.
Using the constraints on the EOS of SNM at suprasaturation densities from
heavy-ion collisions together with the data of finite nuclei and the existence
of $2M_\odot$ neutron stars from electromagnetic (EM) observations, we show
that the high-density symmetry energy cannot be too soft, which leads to lower
bounds on dimensionless tidal deformability of $\Lambda_{1.4} \ge 193$ and
radius of $R_{1.4} \ge 11.1$ km for $1.4M_\odot$ neutron star. Furthermore, we
find that the recent constraint of $\Lambda_{1.4} \le 580$ from the
gravitational wave signal GW170817 detected from the binary neutron star merger
by the LIGO and Virgo Collaborations rules out too stiff high-density symmetry
energy, leading to an upper limit of $R_{1.4} \le 13.3$ km. All these
terrestrial nuclear experiments and astrophysical observations based on strong,
EM and gravitational measurements together put stringent constraints on the
high-density symmetry energy and the EOS of SNM, pure neutron matter and
neutron star matter.
