On Large Trees with Minimal Atom-Bond Connectivity Index

Abstract

Finding trees with minimal atom-bond connectivity (ABC) index, in the general case, is still an open problem. I. Gutman and B. Furtula [MATCH Commun. Math. Comput. Chem. 86 (2012) 131-136] posed a conjecture on the structure of trees with a single high-degree vertex and smallest ABC index. Here we find a case when this conjecture fails for trees with more than 1185 vertices.