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Atom-bond connectivity index of trees. (English) Zbl 1209.05252
Summary: The recently introduced atom-bond connectivity $\left(ABC\right)$ 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 Topological graph theory 92E10 Molecular structures