  We consider the coherent exciton transport, modeled by continuous-time
quantum walks, on Erd\"{o}s-R\'{e}ny graphs in the presence of a random
distribution of traps. The role of trap concentration and of the substrate
dilution is deepened showing that, at long times and for intermediate degree of
dilution, the survival probability typically decays exponentially with a
(average) decay rate which depends non monotonically on the graph connectivity;
when the degree of dilution is either very low or very high, stationary states,
not affected by traps, get more likely giving rise to a survival probability
decaying to a finite value. Both these features constitute a qualitative
difference with respect to the behavior found for classical walks.
