Mean first-passage time on loopless aggregates

We study the mean first-passage time (MFPT) for random walks on the backbone of loopless aggregates. We derive an exact expression for the MFPT on a general aggregate model. The exact MFPT for several deterministic and random disordered structures is calculated. We find that, in general, the exponent τ(1) describing the asymptotic dependence of the MFPT on the linear size of the system for diffusion is τ(1)=1+$d_f$, where $d_f$ is the fractal dimension of the aggregate.