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 xi d(G) = n-ary sumation vEV(G) epsilon G(v)DG(v), where epsilon G(v) is the eccentricity of the vertex v and DG(v) = n-ary sumation uEV(G) dG(u, v) is the sum of all distances from the vertex v. We denote the set of trees with order n and maximum degree increment by Tn, increment . In 2015, the tree having the maximal EDS among all trees in Tn, increment was determined (Miao, 2015). In this paper, the tree having the second maximal EDS among all trees in Tn, increment is characterized. (c) 2024 Elsevier B.V. All rights reserved.