Some further results on the eccentric distance sum

Let G = (V (G), E(G)) be a simple connected graph. Then the eccentric distance sum of G, which is a novel graph invariant by offering a great potential for structure = EvEv activity/property relationships, is defined as xi(d)(G) = Sigma(nu is an element of v) epsilon G (G)DG (v), where epsilon(G) (v) is the eccentricity of the vertex v, and DG (nu) is the sum of all distance from the vertex v. As a continuation to the parts of [22] (Li et al., J. Math. Anal. Appl. 43:1149-1162, 2015), and [17] (Hua et al., Discrete Appl. Math. 160:170-180, 2012), this paper answers one of some remaining problems in [22] is how to determine the bipartite graphs of even diameter with the minimum EDS, and gives a Nordhaus-addum bound for eccentric distance sum, which is the generalization of the corresponding results in [17]. Moreover, some sharp lower bounds on the EDS of Hahn graphs, and of triangle -free and quadrangle-free graphs are respectively presented. (C) 2018 Elsevier Inc. All rights reserved.