On Atom-Bond Connectivity Index

By Bo Zhou, Rundan Xing. 2011

122 citations recorded by the source corpus.

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.

Subfields: Computational Theory and Mathematics, Geometry and Topology, Organic Chemistry

View Paper: https://www.semanticscholar.org/paper/3dbc8577434f6af8254eeb50c6596ee27f677c14

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In Computational Theory and Mathematics

In Geometry and Topology

In Organic Chemistry

Citations in the corpus

On the Augmented Zagreb Index (2014, background): “Details about this index can be found in (Furtula et al., 2012; Hosseini et al., 2014; Lin et al., 2013; Dimitrov, 2013, 2014; Chen & Guo, 2012; Gutman et al., 2013; Imran et al., 2014; Das et al., 2012; Chen et al., 2012) and related references cited therein.”
The ABC Index Conundrum (2013, background): “/ Filomat 27:6 (2013), 1075–1083 1076 In the last few years there is an increased interest for the mathematical properties of the ABC index, resulting in quite a few published papers [1, 2, 4–10, 15–19, 21, 22, 25, 26, 29–32, 34].”
On the degree based topological indices of benzene ring embedded in P-type-surface in 2D network (2017, background): “ABC index is of much importance due to its correlation with the thermodynamic properties of alkanes, see [12, 19].”
Trees with Smallest Atom-Bond Connectivity Index (2012, background): “Recently a long series of mathematical investigations of the ABC index was communicated [3–9,11–14].”
A Resistive Upper Bound for the ABC Index (2014, background): “(For all graph theoretical terms the reader is referred to reference [8]) The index ABC(G) has been studied in a large number of references of which we mention [9], [10] and [11] for their own interest and for many other related references found in them.”
Notes on Trees with Minimal Atom-Bond Connectivity Index (2012, background): “ABC-index were determined [13].”