The forget time for random walks on trees of a fixed diameter

A mixing measure is the expected length of a random walk on a graph given a set of starting and stopping conditions. We study a mixing measure called the forget time. Given a graph G, the pessimal access time for a target distribution is the expected length of an optimal stopping rule to that target distribution, starting from the worst initial vertex. The forget time of G is the smallest pessimal access time among all possible target distributions. We prove that the balanced double broom maximizes the forget time on the set of trees on n vertices with diameter d. We also give a precise formula for the forget time of a balanced double broom