  We study unbiased discrete random walks on the FSFT based on the its
self-similar structure and the relations between random walks and electrical
networks. First, we provide new methods to derive analytic solutions of the
MFPT for any pair of nodes, the MTT for any target node and MDT for any
starting node. And then, using the MTT and the MDT as the measures of trapping
efficiency and diffusion efficiency respectively, we analyze the effect of
trap's position on trapping efficiency and the effect of starting position on
diffusion efficiency. Comparing the trapping efficiency and diffusion
efficiency among all nodes of FSFT, we find the best (or worst) trapping sites
and the best (or worst) diffusing sites. Our results show that: the node which
is at the center of FSFT is the best trapping site, but it is also the worst
diffusing site. The nodes which are the farthest nodes from the two hubs are
the worst trapping sites, but they are also the best diffusion sites. Comparing
the maximum and minimum of MTT and MDT, we found that the maximum of MTT is
almost $\frac{20m^2+32m+12}{4m^2+4m+1}$ times of the minimum of MTT, but the
the maximum of MDT is almost equal to the minimum of MDT. These results shows
that the position of target node has big effect on trapping efficiency, but the
position of starting node almost has no effect on diffusion efficiency. We also
conducted numerical simulation to test the results we have derived, the results
we derived are consistent with those obtained by numerical simulation.
