首页|The evolution of the structure of ABC-minimal trees
The evolution of the structure of ABC-minimal trees
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NSTL
Elsevier
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 is considered by some as one of the most intriguing open problems in mathematical chemistry. In this paper, we describe the exact structure of the extremal trees with sufficiently many vertices and we show how their structure evolves when the number of vertices grows. An interesting fact is that their radius is at most 5 and that all vertices except for one have degree at most 54. In fact, all but at most O(1) vertices have degree 1, 2, 4, or 53. Let gamma(n) = min{ABC(T) : T is a tree of order n}. It is shown that gamma(n) = 1/365 root 1/53 (1 + 26 root 55+ 156 root 106)n + O(1) approximate to 0.67737178 n + O(1). (C) 2021 Elsevier Inc. All rights reserved.
Atom Bond ConnectivityABC indexTopological indexMathematical ChemistryATOM-BOND CONNECTIVITYLAPLACIAN-ENERGYPENDENT PATHSINDEXCONJECTURE
Hosseini, Seyyed Aliasghar、Mohar, Bojan、Ahmadi, Mohammad Bagher
NSTL
Elsevier
