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  • The structure of ABC-minimal trees with given number of leaves
    Mohar, Bojan, 1956-
    The atom-bond connectivity (ABC) index is a degree-based molecular descriptor with diverse chemical applications. Recent work of Lin et al. [W. Lin, J. Chen, C. Ma, Y. Zhang, J. Chen, D. Zhang, and ... F. Jia, On trees with minimal ABC index among trees with given number of leaves, MATCH Commun. Math. Comput. Chem. 76 (2016) 131-140] gave rise to a conjecture about the minimum possible ABC-index of trees with a fixed number ▫$t$▫ of leaves. We show that this conjecture is incorrect and we prove what the correct answer is. It is shown that the extremal tree ▫$T_t$▫ is unique for ▫$t \ge 1195$▫, it has order ▫$|T_t| = t + \lfloor \tfrac{t}{10}\rfloor +1$▫ (when ▫$t$▫ mod 10 is between 0 and 4 or when it is 5, 6, or 7 and ▫$t$▫ is sufficiently large) or ▫$|T_t| = t + \lfloor \tfrac{t}{10}\rfloor + 2$▫ (when ▫$t$▫ mod 10 is 8 or 9 or when it is 5, 6, or 7 and ▫$t$▫ is sufficiently small) and its ABC-index is ▫$( \sqrt{\tfrac{10}{11}} + \tfrac{1}{10}\sqrt{\tfrac{1}{11}} )t + O(1)$▫.
    Vir: Match : communications in mathematical and in computer chemistry. - ISSN 0340-6253 (Vol. 79, no. 2, 2018, str. 415-430)
    Vrsta gradiva - članek, sestavni del ; neleposlovje za odrasle
    Leto - 2018
    Jezik - angleški
    COBISS.SI-ID - 18272089

    Povezava(-e):

    http://match.pmf.kg.ac.rs/electronic_versions/Match79/n2/match79n2_415-430.pdf

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