Efficient computation of trees with minimal atom-bond connectivity index

The atom-bond connectivity (ABC) index is one of the recently most investigated degree-based molecular structure descriptors, that have applications in chemistry. For a graph G, the ABC index is defined as ∑ uv∈E(G) √ (d(u)+d(v)−2) d(u)d(v) , where d(u) is the degree of vertex u in G and E(G) is the set of edges of G. Despite many attempts in the last few years, it is still an open problem to characterize trees with minimal ABC index. In this paper, we present an efficient approach of computing trees with minimal ABC index, by considering the degree sequences of trees and some known properties of the graphs with minimal ABC index. The obtained results disprove some existing conjectures end suggest new ones to be set.