Abstract
For a tree T of order n, let Ω(T)={X∈Ω n∣X⩽A(T)+I n} , where Ω n 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 P n denote the path of length n−1 and K 1, n−1 the complete bipartite graph on 1+( n−1) vertices. In this paper, it is shown that P n and K 1, n−1 are the only trees with minimal and maximal μ-values respectively among all trees of order n.
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