We study numerically the phase-ordering kinetics following a temperature quench of the Ising model with single spin flip dynamics on a class of graphs, including geometrical fractals and random fractals, such as the percolation cluster. For each structure we discuss the scaling properties and compute the dynamical exponents. We show that the exponent $a_chi$ for the integrated response function, at variance with all the other exponents, is independent on temperature and on the presence of pinning. This universal character suggests a strict relation between $a_chi$ and the topological properties of the networks, in analogy to what observed on regular lattices.
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