The atom-bond connectivity (ABC) index of a graph G = (V,E) is defined as ABC(G) = Sigma(vivj is an element of E)root[d(v(i)) + d(v(j)) -2]/[d(v(i))d(v(j))], where d(v(i)) denotes the degree of vertex v(i) of G. This recently introduced molecular structure descriptor found interesting applications in chemistry. However, the problem of characterizing trees with minimal ABC index remains open. In attempts to guess the general structure of such trees, some computer search algorithms were developed. Dimitrov [Appl. Math. Comput. 224 (2013)] presented an algorithm based on tree degree sequences. In this paper we improve this algorithm. Our algorithm generates only less than 2% tree degree sequences, and can find all the n -vertex tree(s) with minimal ABC index for n <= 350 within 8 days. Our search results support Dimitrov's "modulo 7 conjecture" concerning trees with minimal ABC index, and disprove a conjecture we proposed before.
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