  We consider a simple random walk on the T-fractal and we calculate the exact
mean time $\tau^g$ to first reach the central node $i_0$. The mean is performed
over the set of possible walks from a given origin and over the set of starting
points uniformly distributed throughout the sites of the graph, except $i_0$.
By means of analytic techniques based on decimation procedures, we find the
explicit expression for $\tau^g$ as a function of the generation $g$ and of the
volume $V$ of the underlying fractal. Our results agree with the asymptotic
ones already known for diffusion on the T-fractal and, more generally, they are
consistent with the standard laws describing diffusion on low-dimensional
structures.
