A solution of the conjecture about big vertices of minimal-ABC trees

摘要

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.