In this paper, we study the coupling constants of quantized gravitational waves during its scattering and absorption by the black hole in string theory. In string theory, the quantized gravitational waves are closed strings of Planck size which are usually graviton particles in quantum gravity having spin 2. The coupling constants calculated in this paper in terms of winding number of the closed string have been found to form a particular sequence and have shown that they are cyclic vectors. We have calculated various sequences of the coupling constants of gravitational waves which come under the area of metric spaces. We have used the concepts of both T-duality and S-duality in order to explain both scattering and absorption of gravitational waves by the black hole.