  The Vicsek fractals are one of the most interesting classes of fractals and
the study of their structural properties is important. In this paper, the exact
formula for the mean geodesic distance of Vicsek fractals is found. The
quantity is computed precisely through the recurrence relations derived from
the self-similar structure of the fractals considered. The obtained exact
solution exhibits that the mean geodesic distance approximately increases as an
exponential function of the number of nodes, with the exponent equal to the
reciprocal of the fractal dimension. The closed-form solution is confirmed by
extensive numerical calculations.
