Let G=(VG,EG) be a simple connected graph. The eccentric distance sum of G is defined as ~(ξd)(G)= Σv∈~(VG)G(v)~(DG)(v), where ~(εG)(v) is the eccentricity of the vertex v and ~(DG)(v)=Σ~(VG dG)(u,v) is the sum of all distances from the vertex v. In this paper the tree among n-vertex trees with domination number γ having the minimal eccentric distance sum is determined and the tree among n-vertex trees with domination number γ satisfying n=kγ having the maximal eccentric distance sum is identified, respectively, for k=2,3,n3,n2. Sharp upper and lower bounds on the eccentric distance sums among the n-vertex trees with k leaves are determined. Finally, the trees among the n-vertex trees with a given bipartition having the minimal, second minimal and third minimal eccentric distance sums are determined, respectively.
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