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Atom-bond connectivity index of trees. (English) Zbl 1209.05252

Summary: The recently introduced atom-bond connectivity \((ABC)\) index has been applied up to now to study the stability of alkanes and the strain energy of cycloalkanes. Here, mathematical properties of the \(ABC\) index of trees are studied. Chemical trees with extremal \(ABC\) values are found. In addition, it has been proven that, among all trees, the star tree, \(S_n\), has the maximal \(ABC\) value.

MSC:

05C90 Applications of graph theory
05C05 Trees
05C10 Planar graphs; geometric and topological aspects of graph theory
92E10 Molecular structure (graph-theoretic methods, methods of differential topology, etc.)
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References:

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