On structural properties of trees with minimal atom-bond connectivity index IV: Solving a conjecture about the pendent paths of length three

Darko Dimitrov

Applied Mathematics and Computation, 2017, vol. 313, issue C, 418-430

Abstract: The atom-bond connectivity (ABC) index is one of the most investigated degree-based molecular structure descriptors with a variety of chemical applications. It is known that among all connected graphs, the trees minimize the ABC index. However, a full characterization of trees with a minimal ABC index is still an open problem. By now, one of the proved properties is that a tree with a minimal ABC index may have, at most, one pendent path of length 3, with the conjecture that it cannot be a case if the order of a tree is larger than 1178. Here, we provide an affirmative answer of a strengthened version of that conjecture, showing that a tree with minimal ABC index cannot contain a pendent path of length 3 if its order is larger than 415.

Keywords: Molecular structure descriptors; Atom-bond connectivity index; Extremal graphs (search for similar items in EconPapers)
Date: 2017
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Citations: View citations in EconPapers (2)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:313:y:2017:i:c:p:418-430

DOI: 10.1016/j.amc.2017.06.014

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