  The spectral zeta function of the Laplacian on self-similar fractal sets has
been previously studied and shown to meromorphically extend to the complex
plane. In this work we establish under certain conditions a relationship
between the logarithm of the determinant of the discrete graph Laplacian on the
sequence of graphs approximating the fractal and the regularized determinant
which is defined via help of the spectral zeta function. We then at the end
present some concrete examples of this phenomenon.
