The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and is considered by some as one of the most intriguing open problems in mathematical chemistry. In this paper, we describe the exact structure of the extremal trees with sufficiently many vertices and we show how their structure evolves when the number of vertices grows. An interesting fact is that their radius is at most 5 and that all vertices except for one have degree at most 54. In fact, all but at most $O(1)$ vertices have degree 1, 2, 4, or 53. Let ${\gamma }_n=\min \{\mathcal{ABC}(T):T\mathrm{\text{is a tree of order}}n\}$. It is shown that ${\gamma }_n=\frac{1}{365}\sqrt{\frac{1}{53}}(1+26\sqrt{55}+156\sqrt{106})n+O(1)\approx 0.67737178n+O(1)$.

原子键连接 (ABC) 指数是一种基于程度的分子描述符，它发现了多种化学应用。即使经过认真的尝试，用最小 ABC 指数表征树仍然是一个难以捉摸的开放问题，并且被一些人认为是数学化学中最有趣的开放问题之一。在本文中，我们描述了具有足够多顶点的极值树的确切结构，并展示了当顶点数量增加时它们的结构如何演变。一个有趣的事实是，它们的半径最多为 5，并且除一个顶点外，所有顶点的度数最多为 54。事实上，所有顶点都最多为$哦(1)$ 顶点的度数为 1、2、4 或 53。令 ${\gamma }_n=\mathrm{分钟}\{\mathcal{美国广播公司}(吨)：吨\mathrm{\text{是一棵秩序树}}n\}$. 它表明${\gamma }_n=\frac{1}{365}\sqrt{\frac{1}{53}}(1+26\sqrt{55}+156\sqrt{106})n+哦(1)\approx 0.67737178n+哦(1)$.