  We study the phase-ordering kinetics following a temperature quench of O(N)
continuous symmetry models with and 4 on graphs. By means of extensive
simulations, we show that the global pattern of scaling behaviours is analogous
to the one found on usual lattices. The exponent a for the integrated response
function and the exponent z, describing the growing length, are related to the
large scale topology of the networks through the spectral dimension and the
fractal dimension alone, by means of the same expressions as are provided by
the analytic solution of the inifnite N limit. This suggests that the large N
value of these exponents could be exact for every N.
