Given an n-vertex graph G, the matrix Omega(G) = (I-n + L(G))(-1) = (omega(ij)) is called the doubly stochastic graph matrix of G, where I-n is the n x n identity matrix and L(G) is the Laplacian matrix of G. Let omega(G) be the smallest element of Omega(G). Zhang and Wu [X.D. Zhang and J.X. Wu. Doubly stochastic matrices of trees. Appl. Math. Lett., 18:339-343, 2005.] determined the tree T with the minimum omega(T) among all the n-vertex trees. In this paper, as a continuance of the Zhang and Wu's work, we determine the first. inverted left perepndiculern-1/2inverted right perpendicular trees...
