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Maximal augmented Zagreb index of trees with given diameter

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  • Jiang, Yisheng
  • Lu, Mei

Abstract

Let G=(V,E) be an n-vertex graph, where V={v0,v1,…,vn−1}. The augmented Zagreb index (AZI) of G is defined as AZI(G)=∑vivj∈E[didj/(di+dj−2)]3, where di is the degree of vi. Let Tnd be the set of all trees on n vertices with given diameter d. In this paper, we determine the tree with maximum AZI among Tnd when n≥32(d−1)+381. Our result partially resolve a problem given in [12].

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  • Jiang, Yisheng & Lu, Mei, 2021. "Maximal augmented Zagreb index of trees with given diameter," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    • Handle: RePEc:eee:apmaco:v:395:y:2021:i:c:s0096300320308080
    DOI: 10.1016/j.amc.2020.125855
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    References listed on IDEAS

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    1. Palacios, José Luis, 2017. "Bounds for the augmented Zagreb and the atom-bond connectivity indices," Applied Mathematics and Computation, Elsevier, vol. 307(C), pages 141-145.
    2. Sun, Xiaoling & Gao, Yubin & Du, Jianwei & Xu, Lan, 2018. "Augmented Zagreb index of trees and unicyclic graphs with perfect matchings," Applied Mathematics and Computation, Elsevier, vol. 335(C), pages 75-81.
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    Cited by:

    1. Li, Shuchao & Wang, Zheng & Zhang, Minjie, 2022. "On the extremal Sombor index of trees with a given diameter," Applied Mathematics and Computation, Elsevier, vol. 416(C).

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