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BY-NC-ND 3.0 license Open Access Published by De Gruyter June 2, 2014

On Atom-Bond Connectivity Index

  • Bo Zhou EMAIL logo and Rundan Xing

The atom-bond connectivity (ABC) index, introduced by Estrada et al. in 1998, displays an excellent correlation with the formation heat of alkanes. We give upper bounds for this graph invariant using the number of vertices, the number of edges, the Randi´c connectivity indices, and the first Zagreb index. We determine the unique tree with the maximum ABC index among trees with given numbers of vertices and pendant vertices, and the n-vertex trees with the maximum, and the second, the third, and the fourth maximum ABC indices for n ≥ 6.

Received: 2010-1-23
Revised: 2010-6-5
Published Online: 2014-6-2
Published in Print: 2011-2-1

© 1946 – 2014: Verlag der Zeitschrift für Naturforschung

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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