Let G=(VG,EG) be a simple connected graph. The eccentric distance sum of G is defined as ξd(G)= Σv∈VGG(v)DG(v), where εG(v) is the eccentricity of the vertex v and DG(v)=ΣVG 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 bou...
