Complete characterization of the minimal-ABC trees

The problem of complete characterization trees with minimal atom-bond-connectivity index (minimal-ABC trees) is a long-standing open problem. Here firstly, we give an affirmative answer to the conjecture, which states that enough large minimal-ABC are comprised solely root vertex and so-called Dz- Dz+1-branches. Based on presented theoretical results here some already known results, obtain constraints reduce search space solve optimization problem, thus, determine exactly given arbitrary order.