The generating functions of hitting times for random walk on trees

In this paper, using the first-step analysis, we provide the probability generating functions of hitting and cover times for simple random walk (SRW) on path. Furthermore, we give an algorithm to calculate the probability generating functions of hitting times for SRW on general trees, and two illustrative examples are given. Then we show that the expectations and variances of hitting times for SRW on trees are all integers.