On the eccentric connectivity index and Wiener index of a graph

P. Dankelmann, M. J. Morgan, S. Mukwembi, H. C. Swart

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19 Citations (Scopus)


Let G be a finite connected graph of order n and minimum degree δ. The eccentric connectivity index ξc (G) of G is defined as ξc (G) = Σv{small element of}V (G) ecG (v)degG (v), where ecG (x) and degG (x) denote the eccentricity and degree of vertex x in G, respectively. We prove that the eccentric connectivity index of G satisfies, and construct graphs which asymptotically attain the bound. Our bound implies some known results by Došlić, Saheli & Vukičević [4], Morgan, Mukwembi & Swart [11], and Zhou & Du [16]. Further, we also determine upper bounds on the well-studied Wiener index in terms of the eccentric connectivity index.

Original languageEnglish
Pages (from-to)39-47
Number of pages9
JournalQuaestiones Mathematicae
Issue number1
Publication statusPublished - Jan 2014


  • Eccentricity
  • eccentric connectivity index
  • minimum degree

ASJC Scopus subject areas

  • Mathematics (miscellaneous)


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