  We study discrete random walks on the NFSFT and provide new methods to
calculate the analytic solutions of the MFPT for any pair of nodes, the MTT for
any target node and MDT for any source node. Further more, using the MTT and
the MDT as the measures of trapping efficiency and diffusion efficiency
respectively, we compare the trapping efficiency and diffusion efficiency for
any two nodes of NFSFT and find the best (or worst) trapping sites and the best
(or worst) diffusion sites. Our results show that: the two hubs of NFSFT is the
best trapping site, but it is also the worst diffusion 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 ratio between the maximum and minimum of MTT grows
logarithmically with network order, but the ratio between the maximum and
minimum of MTT is almost equal to $1$. These results implie that the trap's
position has great effect on the trapping efficiency, but the position of
source 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.
