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On bond incident degree index of chemical trees with a fixed order and a fixed number of leaves

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  • Du, Jianwei
  • Sun, Xiaoling

Abstract

A tree in which no vertex has a degree greater than 4 is called a chemical tree. The bond incident degree index of a chemical tree T is defined as ∑xy∈ETφ(degT(x),degT(y)), where ET is the edge set of T, φ is a real-valued symmetric function, and degT(x) stands for the degree of a vertex x of T. This paper reports extremal results on bond incident degree indices of chemical trees with a fixed order and a fixed number of leaves. Furthermore, we use these results directly to some renowned topological indices, such as symmetric division deg index, Randić index, geometric-arithmetic index, sum-connectivity index, Sombor index, harmonic index, multiplicative sum Zagreb index, atom-bond connectivity index, etc.

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  • Du, Jianwei & Sun, Xiaoling, 2024. "On bond incident degree index of chemical trees with a fixed order and a fixed number of leaves," Applied Mathematics and Computation, Elsevier, vol. 464(C).
    • Handle: RePEc:eee:apmaco:v:464:y:2024:i:c:s0096300323005593
    DOI: 10.1016/j.amc.2023.128390
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    References listed on IDEAS

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    1. Cruz, Roberto & Monsalve, Juan & Rada, Juan, 2020. "Extremal values of vertex-degree-based topological indices of chemical trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
    2. Vujošević, Saša & Popivoda, Goran & Kovijanić Vukićević, Žana & Furtula, Boris & Škrekovski, Riste, 2021. "Arithmetic–geometric index and its relations with geometric–arithmetic index," Applied Mathematics and Computation, Elsevier, vol. 391(C).
    3. Chen, Xiaohong, 2023. "General sum-connectivity index of a graph and its line graph," Applied Mathematics and Computation, Elsevier, vol. 443(C).
    4. Du, Jianwei & Sun, Xiaoling, 2022. "Extremal symmetric division deg index of molecular trees and molecular graphs with fixed number of pendant vertices," Applied Mathematics and Computation, Elsevier, vol. 434(C).
    5. Dimitrov, Darko & Du, Zhibin, 2021. "A solution of the conjecture about big vertices of minimal-ABC trees," Applied Mathematics and Computation, Elsevier, vol. 397(C).
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    Cited by:

    1. Das, Kinkar Chandra, 2024. "Open problems on Sombor index of unicyclic and bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 473(C).

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