  We perform an explicit one-loop calculation for the gravitational
contributions to the two-, three- and four-point gauge Green's functions with
paying attention to the quadratic divergences. It is shown for the first time
in the diagrammatic calculation that the Slavnov-Taylor identities are
preserved even if the quantum graviton effects are included at one-loop level,
such a conclusion is independent of the choice of regularization schemes. We
also present a regularization scheme independent calculation based on the gauge
condition independent background field framework of Vilkovisky-DeWitt's
effective action with focusing on both the quadratic divergence and quartic
divergence that is not discussed before. With the harmonic gauge condition, the
results computed by using the traditional background field method can
consistently be recovered from the Vilkovisky-DeWitt's effective action
approach by simply taking a limiting case, and are found to be the same as the
ones yielded by the diagrammatic calculation. As a consequence, in all the
calculations, the symmetry-preserving and divergent-behavior-preserving loop
regularization method can consistently lead to a nontrivial gravitational
contribution to the gauge coupling constant with an asymptotic free power-law
running at one loop near the Planck scale.
