On structural properties of trees with minimal atom-bond connectivity index II (original) (raw)

The atom-bond connectivity (ABC) index is a degree-based graph topological index that found chemical applications. The problem of complete characterization of trees with minimal ABC index is still an open problem. In [14], it was shown that trees with minimal ABC index do not contain so-called B k-branches, with k ≥ 5, and that they do not have more than four B 4-branches. Our main results here reveal that the number of B 1 and B 2-branches are also bounded from above by small fixed constants. Namely, we show that trees with minimal ABC index do not contain more than four B 1-branches and more than eleven B 2-branches.