  Determining and analyzing the spectra of graphs is an important and exciting
research topic in theoretical computer science. The eigenvalues of the
normalized Laplacian of a graph provide information on its structural
properties and also on some relevant dynamical aspects, in particular those
related to random walks. In this paper, we give the spectra of the normalized
Laplacian of iterated subdivisions of simple connected graphs. As an example of
application of these results we find the exact values of their multiplicative
degree-Kirchhoff index, Kemeny's constant and number of spanning trees.
