The problem of full determination of trees with a minimal value of the ABC index is very hard and famous in mathematical chemistry. A well-known conjecture is that the big vertices (vertices of degree larger than 2, which are not adjacent to a vertex of degree 2) of a tree with a minimal value of the ABC index induce a star graph. Here we give an affirmative answer to this conjecture and thus make a significant step towards the complete characterization of trees with minimal ABC index.

中文翻译：

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关于极小ABC树的大顶点的猜想的一个解

用ABC指数的最小值完全确定树木的问题是非常困难的，在数学化学中也很著名。一个众所周知的猜想是，具有最小ABC索引值的树的大顶点（大于2的顶点，不与2的顶点相邻）会产生星形图。在这里，我们对这个猜想给出肯定的答案，从而朝着具有最小ABC指数的树木的完整表征迈出了重要的一步。