  The possibility of superconducting pairing of electrons in doped graphene due
to in-plane and out-of-plane phonons is studied. Quadratic coupling of
electrons with out-of-plane phonons is considered in details, taking into
account both deformation potential and bond-stretch contributions. The order
parameter of electron-electron pairing can have different structures due to
four-component spinor character of electrons wave function. We consider s-wave
pairing, diagonal on conduction and valence bands, but having arbitrary
structure with respect to valley degree of freedom. The sign and magnitude of
contribution of each phonon mode to effective electron-electron interaction
turns out to depend on both the symmetry of phonon mode and the structure of
the order parameter. Unconventional orbital-spin symmetry of the order
parameter is found.
