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

Authors

  • du Toit, Lindie
  • Mukwembi, Simon
  • Vetrík, Tomáš

Abstract

The eccentric connectivity index of a graph G is defined as ECI(G) = Σv∊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.

Published

2020-06-09

How to Cite

du Toit, Lindie, Mukwembi, Simon, & Vetrík, Tomáš. (2020). A note on the eccentric connectivity index of graphs of given diameter. Utilitas Mathematica, 115. Retrieved from https://utilitasmathematica.com/index.php/Index/article/view/1494

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