On structural properties of trees with minimal atom-bond connectivity index II: Bounds on - and -branches

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• 作者：Darko Dimitrov ^{darko.dimitrov11@gmail.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Atom-bond connectivity index ; Topological indices ; Extremal graphs
• 刊名：Discrete Applied Mathematics
• 出版年：2016
• 出版时间：11 May 2016
• 年：2016
• 卷：204
• 期：Complete
• 页码：90-116
• 全文大小：875 K

文摘

The atom-bond connectivity (ABC) index   is a degree-based topological index that found chemical applications. The problem of complete characterization of trees with minimal ABC$ABC$ index is still an open problem. In an earlier paper, it was shown that trees with minimal ABC index do not contain so-called B_k$B_k$-branches  , with k≥5$k\ge 5$, and that they do not have more than four B₄$B_4$-branches. Our main results here reveal that the number of B₁$B_1$ and B₂$B_2$-branches are also bounded from above by small fixed constants. Namely, we show that trees with minimal ABC index do not contain more than four B₁$B_1$-branches and more than eleven B₂$B_2$-branches.