A note on the eccentric connectivity index of graphs of given diameter

Abstract

The eccentric connectivity index of a graph G is defined as ECI(G) = Σ_v∊v(G) ec(v)deg(v), where V(G) is the vertex set of G, deg(v) is the degree of a vertex v and ec(v) is the eccentricity of v. The eccentric connectivity index of various graphs has been extensively studied especially in the last decade. We present upper bounds on the eccentric connectivity index for graphs of given order and fixed diameter. We also show that our bounds are asymptotically sharp. © 2020 Utilitas Mathematica Publishing Inc.. All rights reserved.