## Abstract

Let G be a finite connected graph of order n and minimum degree δ. The eccentric connectivity index ξ^{c} (G) of G is defined as ξ^{c} (G) = Σ_{v{small element of}V (G)} ec_{G} (v)deg_{G} (v), where ec_{G} (x) and deg_{G} (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 language | English |
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Pages (from-to) | 39-47 |

Number of pages | 9 |

Journal | Quaestiones Mathematicae |

Volume | 37 |

Issue number | 1 |

DOIs | |

Publication status | Published - Jan 2014 |

## Keywords

- Eccentricity
- eccentric connectivity index
- minimum degree

## ASJC Scopus subject areas

- Mathematics (miscellaneous)