  In this paper, we consider discrete time random walks on the pseudofractal
scale-free web (PSFW) and we study analytically the related first passage
properties. First, we classify the nodes of the PSFW into different levels and
propose a method to derive the generation function of the first passage
probability from an arbitrary starting node to the absorbing domain, which is
located at one or more nodes of low-level (i.e., nodes with large degree).
Then, we calculate exactly the first passage probability, the survival
probability, the mean and the variance of first passage time by using the
generating functions as a tool. Finally, for some illustrative examples
corresponding to given choices of starting node and absorbing domain, we derive
exact and explicit results for such first passage properties. The method we
propose can as well address the cases where the absorbing domain is located at
one or more nodes of high-level on the PSFW, and it can also be used to
calculate the first passage properties on other networks with self-similar
structure, such as $(u, v)$ flowers and recursive scale-free trees.
