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Fractal phenomena may be widely observed in a great number of complexsystems. In this paper, we revisit the well-known Vicsek fractal, and studysome of its structural properties for purpose of understanding how theunderlying topology influences its dynamic behaviors. For instance, weanalytically determine the exact solution to mean first-passage time for randomwalks on Vicsek fractal in a more light mapping-based manner than previousother methods, including typical spectral technique. More importantly, ourmethod can be quite efficient to precisely calculate the solutions to meanfirst-passage time on all generalized versions of Vicsek fractal generatedbased on an arbitrary allowed seed, while other previous methods suitable fortypical Vicsek fractal will become prohibitively complicated and even fail.Lastly, this analytic results suggest that the scaling relation between meanfirst-passage time and vertex number in generalized versions of Vicsek fractalkeeps unchanged in the large graph size limit no matter what seed is selected.

Exact mean first-passage time on generalized Vicsek fractal