ABC Index of Trees with Fixed Number of LeavesMATCH Communications in Mathematical and in Computer Chemistry
AbstractGiven 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.
Citation InformationMikhail Goubko, Colton Magnant, Pouria Salehi Nowbandegani and Ivan Gutman. "ABC Index of Trees with Fixed Number of Leaves" MATCH Communications in Mathematical and in Computer Chemistry Vol. 74 Iss. 3 (2015) p. 697 - 702
Available at: http://works.bepress.com/colton_magnant/50/