On the Maximal Eccentric Distance Sums of Graphs

If is a simple connected graph with vertex (), then the eccentric distance sum of , denoted by (), is defined as ∑∈()ec()(), where ec() is the eccentricity of the vertex and () is the sum of all distances from the vertex . Let ≥8. We determine the -vertex trees with, respectively, the maximum, second-maximum, third-maximum, and fourth-maximum eccentric distance sums. We also characterize the extremal unicyclic graphs on vertices with respectively, the maximal, second maximal, and third maximal eccentric distance sums.