The evolution of the structure of ABC-minimal trees

The atom-bond connectivity (ABC) index is a degree-based molecular descriptor that found diverse chemical applications. Characterizing trees with minimum ABC-index remained an elusive open problem even after serious attempts and considered by some as one of the most intriguing problems in mathematical chemistry. In this paper, we describe exact structure extremal sufficiently many vertices show how their evolves when number grows. An interesting fact radius at 5 all except for have degree 54. fact, but O(1) 1, 2, 4, or 53. Let γn=min⁡{ABC(T):Tis tree ordern}. It shown γn=1365153(1+2655+156106)n+O(1)≈0.67737178n+O(1).