ABC Index of Trees with Fixed Number of Leaves

Given a graph G, the atom-bond connectivity (ABC) index is defined to be ABC(G) = Sigma Euv is an element of E(G)root d(G)(u)+d(G)(v)-2/d(G)(u)d(G)(v), where E(G) is the edge set of graph G and d(G)(v) is the degree of vertex v in graph G. The paper [10] 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.