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

Eccentric distance sum index for some classes of connected graphs

“…In this paper we presented a lower bound for the eccentric distance sum index for some generalization of cacti. This result extends the result of Hua, Xu and Wen [4] for cacti. There remains an open problem of how to order graphs in a class by the values of the eccentric distance sum index.…”

“…In this section there is a research done for lower bound of the eccentric distance sum index for some generalization of cacti. In Theorem 2.1 we present an interesting result of Hua, Xu and Wen [4] for cacti.…”

“…They proved it also for unicyclic graphs. Hua, Xu, Wen [4] gave then a short and unified proof of their results.…”

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.…”

Chain Hexagonal Cacti with the Extremal Eccentric Distance Sum

“…Li et al [5] investigated the trees with the minimal and second minimal EDS among n -vertex trees with given matching number; as a continuance they also determine the trees with the third and fourth minimal EDS among the n -vertex trees and characterized the trees with the second EDS among the n -vertex trees of a given diameter. For other recent results on EDS, the readers are referred to [6, 7]. …”