On the eccentric distance sum of trees with given maximum degree.

Let G be a simple connected graph. The eccentric distance sum (EDS) of G is defined as ξ d (G) = ∑ v ∈ V (G) ɛ G (v) D G (v) , where ɛ G (v) is the eccentricity of the vertex v and D G (v) = ∑ u ∈ V (G) d G (u , v) is the sum of all distances from the vertex v. We denote the set of trees with order n and maximum degree Δ by T n , Δ. In 2015, the tree having the maximal EDS among all trees in T n , Δ was determined (Miao, 2015). In this paper, the tree having the second maximal EDS among all trees in T n , Δ is characterized. [ABSTRACT FROM AUTHOR]