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On Eccentric Connectivity Index and Connectivity

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Abstract

Let G be a finite connected graph. The eccentric connectivity index ξc(G) of G is defined as ξc(G) = ΣV∈V (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.

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Authors and Affiliations

  1. Department of Mathematics, University of Zimbabwe, Harare, Zimbabwe

    Vivian Mukungunugwa & Simon Mukwembi

Authors
  1. Vivian Mukungunugwa
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  2. Simon Mukwembi
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Correspondence to Vivian Mukungunugwa or Simon Mukwembi.

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Mukungunugwa, V., Mukwembi, S. On Eccentric Connectivity Index and Connectivity. Acta. Math. Sin.-English Ser. 35, 1205–1216 (2019). https://doi.org/10.1007/s10114-019-7320-1

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  • DOI: https://doi.org/10.1007/s10114-019-7320-1

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