Computer search for trees with minimal ABC index

The ABC index is a degree-based molecular structure descriptor, that found chemical applications. Finding the connected graph(s) of a given order whose ABC index is minimal is a hitherto unsolved problem, but it is known that these must be trees. In this paper, by combining mathematical arguments and computer-based modeling we establish the basic structural features of the minimum-ABC trees.

► Atom-bond connectivity (ABC) index is a degree-based graph invariant.
► Connected graphs with minimal ABC are trees.
► Trees with minimal ABC index are determined.