  We completely clarify the feature of primordial non-Gaussianities of tensor
perturbations in generalized G-inflation, i.e., the most general single-field
inflation model with second order field equations. It is shown that the most
general cubic action for the tensor perturbation (gravitational wave) $h_{ij}$
is composed only of two contributions, one with two spacial derivatives and the
other with one time derivative on each $h_{ij}$. The former is essentially
identical to the cubic term that appears in Einstein gravity and predicts a
squeezed shape, while the latter newly appears in the presence of the kinetic
coupling to the Einstein tensor and predicts an equilateral shape. Thus, only
two shapes appear in the graviton bispectrum of the most general single-field
inflation model, which could open a new clue to the identification of
inflationary gravitational waves in observations of cosmic microwave background
anisotropies as well as direct gravitational wave detection experiments.
