Permanents of doubly stochastic trees

For a tree T of order n, let Ω(T)={X Ωn X A(T)+In}, where Ωn denotes the set of all doubly stochastic matrices of order n and A(T) denotes the adjacency matrix of T, and let μ(T) denote the minimum permanent of matrices in Ω(T). Let Pn denote the path of length n−1 and K1,n−1 the complete bipartite graph on 1+(n−1) vertices. In this paper, it is shown that Pn and K1,n−1 are the only trees with minimal and maximal μ-values respectively among all trees of order n.