Target problem on small-world networks

In this work we focus on reactions on small-world networks (SWN’s), disordered graphs of much recent interest. We study the target problem, since it allows an exact solution on regular lattices. On SWN’s we find that the decay of the targets (for which we extend the formalism to disordered lattices) is again related to $S\left(n\right),$ the mean number of distinct sites visited in n steps, although the $S\left(n\right)\mathrm{}$ vs n dependence changes here drastically in going from regular linear chains to their SWN.