The minimum ABC index of chemical trees.

Let G be a graph with vertex set V (G) and edge set E (G). The ABC index of G , denoted by A B C (G) , is defined as A B C (G) = ∑ u v ∈ E (G) d G (u) + d G (v) − 2 d G (u) d G (v) . In [B. Furtula, A. Graovac, D. Vukičević, Atom-bond connectivity index of trees, Discrete Appl. Math. 157 (2009) 2828–2835], the authors gave a lower bound of the ABC index for chemical trees. Noticing that this lower bound is not consistently tight, we completely determine the minimum ABC index for chemical trees of order n ≥ 13. Furthermore, the ABC-minimal chemical trees are also characterized. [ABSTRACT FROM AUTHOR]