The access time of random walks on trees with given partition

Highlights：

• The access time H(π,v) is very hard to obtained in general graphs. In this paper, the access time of trees are investigated and some precise values of access time are obtained for some special trees.

• This paper presents two useful transformations that increase maxvHT(π,v) and decrease minvHT(π,v) respectively, which is not only useful in this paper but is also useful to deal with many similar problems.

• The results of this paper not only get the sharp upper bound of maxvHT(π,v) and the sharp lower bound of minvHT(π,v) among trees with given partition, but also lead to the parallel results among all trees. Therefore, this paper generalizes the known results among all trees in some scence.