  The survival probability of immobile targets, annihilated by a population of
random walkers on inhomogeneous discrete structures, such as disordered solids,
glasses, fractals, polymer networks and gels, is analytically investigated. It
is shown that, while it cannot in general be related to the number of distinct
visited points, as in the case of homogeneous lattices, in the case of bounded
coordination numbers its asymptotic behaviour at large times can still be
expressed in terms of the spectral dimension $\widetilde {d}$, and its exact
analytical expression is given. The results show that the asymptotic survival
probability is site independent on recurrent structures ($\widetilde{d}\leq2$),
while on transient structures ($\widetilde{d}>2$) it can strongly depend on the
target position, and such a dependence is explicitly calculated.
