2017/06/26 by Darko Dimitrov, Dimitrov, Darko
Biochemistry, Genetics and Molecular Biology · Computer Science · Materials Science · Mathematics · #Computational Drug Discovery Methods #Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Graph theory and applications #Machine Learning in Materials Science #Protein Structure and Dynamics
paper · pdf · doi:10.48550/arxiv.1706.08587
openalex publication_date 2017/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The atom-bond connectivity (ABC) index is one of the most investigated\ndegree-based molecular structure descriptors with a variety of chemical\napplications. It is known that among all connected graphs, the trees minimize\nthe ABC index. However, a full characterization of trees with a minimal ABC\nindex is still an open problem. By now, one of the proved properties is that a\ntree with a minimal ABC index may have, at most, one pendent path of length\n3, with the conjecture that it cannot be a case if the order of a tree is\nlarger than 1178. Here, we provide an affirmative answer of a strengthened\nversion of that conjecture, showing that a tree with minimal ABC index cannot\ncontain a pendent path of length 3 if its order is larger than 415.\n