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Given an n-vertex graph G, the matrix (G) = (In + L(G)) −1 = (!ij) is called the doubly stochastic graph matrix of G, where In is the nn identity matrix and L(G) is the Laplacian matrix of G. Let !(G) be the smallest element of (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 !(T) among all the n-vertex trees. In this paper, as a continuance of the Zhang and Wu's work, we determine the first d n−1

Ordering trees by the minimal entries of doubly stochastic graph matrices