ABC Index of Trees with Fixed Number of Leaves
MATCH Communications in Mathematical and in Computer Chemistry
Given a graph G, the atom-bond connectivity (ABC) index is defined to be ABC(G) = P uv∈E(G) qdG(u)+dG(v)−2 dG(u) dG(v) , where E(G) is the edge set of graph G and dG(v) is the degree of vertex v in graph G. The paper  claims to classify tho trees with a fixed number of leaves which minimize the ABC index. Unfortunately, there is a gap in the proof, leading to other examples that contradict the main result of that work. These examples and the problem are discussed in this note.
Goubko, Mikhail, Colton Magnant, Pouria Salehi Nowbandegani, Ivan Gutman.
"ABC Index of Trees with Fixed Number of Leaves."
MATCH Communications in Mathematical and in Computer Chemistry, 74 (3): 697-702.