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Acta Mathematica Sinica, English Series

, Volume 35, Issue 7, pp 1205–1216 | Cite as

On Eccentric Connectivity Index and Connectivity

  • Vivian MukungunugwaEmail author
  • Simon MukwembiEmail author
Article
  • 14 Downloads

Abstract

Let G be a finite connected graph. The eccentric connectivity index ξc(G) of G is defined as ξc(G) = ΣVV (G) ec(v)deg(v), where ec(v) and deg(v) denote the eccentricity and degree of a vertex v in G, respectively. In this paper, we give an asymptotically sharp upper bound on the eccentric connectivity index in terms of order and vertex-connectivity and in terms of order and edge-connectivity. We also improve the bounds for triangle-free graphs.

Keywords

Extremal graph order diameter vertex-connectivity edge-connectivity 

MR(2010) Subject Classification

05C35 05C12 05C40 

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Copyright information

© Institute of Mathematics, Chinese Academy of Sciences and Chinese Mathematical Society 2019

Authors and Affiliations

  1. 1.Department of MathematicsUniversity of ZimbabweHarareZimbabwe

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