The eccentric distance sum of connected graphs

Abstract

The eccentric distance sum (EDS) of a connected graph G is defined as ζ^d(G) = Σ_v∈V(G) ϵ_G(v)D_G(v), where ϵ_G(v) is the eccentricity of a vertex v in G and D_G (v) is the sum of distances between v and all other vertices in G. In this paper, we present several new bounds for EDS in terms of other graph parameters including the Wiener index, Harary index, second multiplicative Zagreb index, multiplicative Wiener index, first Zagreb index, first Zagreb coindex, and so on. Moreover, we compare the eccentric distance sum and degree distance for some connected graphs.