On the eccentric distance sum of graphs

A short and unified proof of Yu et al.ʼs two results on the eccentric distance sum

“…More recently, the mathematical properties of EDS have been investigated [4,5]. In particular, Yu et al [5] characterized the extremal tree and unicyclic graph with respect to EDS among all n-vertex trees and unicyclic graphs, respectively.…”

The eccentric-distance sum of some graphs

“…Hua, Xu and Shu [16] obtained the sharp lower bound on EDS of n-vertex cacti. Ilić, Yu and Feng [20] studied various lower and upper bounds for the EDS in terms of other graph invariant including the Wiener index, the degree distance index, the eccentric connectivity index and so on.…”

Some extremal results on the connective eccentricity index of graphs

“…Moreover, Sharma et al [24] introduced the eccentric connectivity index, for a graph, which has been employed successfully for the development of numerous mathematical models for the prediction of biological activities of diverse nature [13,24,25]. Some nice results on other attractive distance-based topological indices of graphs can be found in [14,16,19,31] for eccentric distance sum, [8] for Zagreb eccentricity indices, [23] for adjacent eccentric distance sum index, [10,18,26,27] for degree distance, [11,15] for Gutman index and a recent survey [28] for extremal problems. Furthermore, some interesting properties of eccentricity are reported in [20,21].…”