Can a neutron decay to the gravitons? Is it possible that a bunch of neutrons totally  decay to the  graviton? In  other words, does the baryon number conserve in the  quantum gravity interactions? 
 A: This is the relative strength of interactions of elementary particles:
strong  1
electromagnetic 1/137
weak 10^-6
gravity  6x10^-39
A free neutron decays through the weak interaction with a lifetime of 14.7 minutes. The gravitational interaction is 10^-33 times weaker than the weak.  In the lifetime computations this would be squared .Even if baryon number conservation were violated by the gravitational interaction, the probability of the decay of the neutron to gravitons is infinitessimally small , due to the extreme  weakness of the gravitational interaction.
A: No, conservation of Baryon number prevents a neutron decaying into gravitons.
A neutron has Baryon number $B=1$. A graviton (or any gauge boson or lepton) has $B=0$. And famously, $1\neq0$.
A: Even if there were a baryon-number-violating process in quantum gravity at low energy (which I think is excluded by the stability of ordinary matter), you couldn't have a single neutron decay to two gravitons because of angular momentum conservation.  The neutron in its rest frame has spin $\hbar/2$, but each graviton has spin $2\hbar$.  No combination of intrinsic and orbital angular momentum for two spin-2 gravitons can reproduce the initial state of a spin-half neutron.
Angular momentum would permit a pair of neutrons to decay to a pair of integer-spin bosons.  However my instinct is that $\rm n+n\to g+g$ would cause stable nuclei to become neutron-deficient over geological timescales.  Our models connecting isotopic abundances on Earth and in space to stellar and big-bang nucleosynthesis agree too well for this process to be important.
The Particle Data Group summarizes limits for the neutron-antineutron ($\rm n\bar n$) oscillation time, which is at least $10^5$ neutron lifetimes.  I think this process, if mediated by scattering from background gravitons, 
$$ \rm n + g \to \bar n + g'$$
would have the same coupling constant as $\rm n+n\to g+g$, but depend on the energy spectrum of the local graviton field.
The PDG also summarizes limits for "neutron to mirror-neutron" ($\rm n n'$) oscillations from "neutron disappearance" experiments, which is closer to your original question; those experiments are harder, so the limits are weak.
