  The gravitational wave (GW) detection of a binary neutron star inspiral made
by the Advanced LIGO and Advanced Virgo paves the unprecedented way for
multi-messenger observations. The propagation speed of this GW can be
scrutinized by comparing the arrival times between GW and neutrinos or photons.
It provides the constraint on the mass of the graviton. f(R) gravity theories
have the habitual non-zero mass gravitons in addition to usual massless ones.
Previously, we show that the model independent f(R) gravity theories can be
constructed from the both background evolution and the matter growth with one
undetermined parameter. We show that this parameter can be constrained from the
graviton mass bound obtained from GW detection. Thus, the GW detection provides
the invaluable constraint on the validity of f(R) gravity theories.
