On the extremal values of the eccentric distance sum of trees

Let GG be a simple connected graph. The eccentric distance sum (EDS) of GG is defined as ξd(G)=∑v∈VεG(v)DG(v)ξd(G)=∑v∈VεG(v)DG(v), where εG(v)εG(v) is the eccentricity of the vertex vv and DG(v)=∑u∈VdG(u,v)DG(v)=∑u∈VdG(u,v) is the sum of all distances from the vertex vv. In this paper, the trees having the maximal EDS among nn-vertex trees with maximum degree ΔΔ and among those with domination number 3 are characterized. The trees having the maximal or minimal EDS among nn-vertex trees with independence number αα and the trees having the maximal EDS among nn-vertex trees with matching number mm are also determined.