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Complete solution to open problems on exponential augmented Zagreb index of chemical trees

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  • Mondal, Sourav
  • Das, Kinkar Chandra

Abstract

One of the crucial problems in combinatorics and graph theory is characterizing extremal structures with respect to graph invariants from the family of chemical trees. Cruz et al. (2020) [7] presented a unified approach to identify extremal chemical trees for degree-based graph invariants in terms of graph order. The exponential augmented Zagreb index (EAZ) is a well-established graph invariant formulated for a graph G asEAZ(G)=∑vivj∈E(G)e(didjdi+dj−2)3, where di signifies the degree of vertex vi, and E(G) is the edge set. Due to some special counting features of EAZ, it was not covered by the aforementioned unified approach. As a result, the exploration of extremal chemical trees for this invariant was posed as an open problem in the same article. The present work focuses on generating a complete solution to this problem. Our findings offer maximal and minimal chemical trees of EAZ in terms of the graph order n.

Suggested Citation

  • Mondal, Sourav & Das, Kinkar Chandra, 2024. "Complete solution to open problems on exponential augmented Zagreb index of chemical trees," Applied Mathematics and Computation, Elsevier, vol. 482(C).
    • Handle: RePEc:eee:apmaco:v:482:y:2024:i:c:s0096300324004442
    DOI: 10.1016/j.amc.2024.128983
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    References listed on IDEAS

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    1. Dehmer, Matthias & Emmert-Streib, Frank & Shi, Yongtang, 2015. "Graph distance measures based on topological indices revisited," Applied Mathematics and Computation, Elsevier, vol. 266(C), pages 623-633.
    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.
    3. 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).
    4. 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).
    5. Roberto Cruz & Juan Daniel Monsalve & Juan Rada, 2021. "The balanced double star has maximum exponential second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 41(2), pages 544-552, February.
    6. Bermudo, Sergio & Cruz, Roberto & Rada, Juan, 2022. "Vertex-degree-based topological indices of oriented trees," Applied Mathematics and Computation, Elsevier, vol. 433(C).
    7. 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).
    8. Ghalavand, Ali & Klavžar, Sandi & Tavakoli, Mostafa & Hakimi-Nezhaad, Mardjan & Rahbarnia, Freydoon, 2023. "Leap eccentric connectivity index in graphs with universal vertices," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    9. Shang, Yilun, 2022. "Sombor index and degree-related properties of simplicial networks," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    10. Jiang, Yisheng & Lu, Mei, 2021. "Maximal augmented Zagreb index of trees with given diameter," Applied Mathematics and Computation, Elsevier, vol. 395(C).
    11. Dehmer, Matthias & Emmert-Streib, Frank & Tratnik, Niko & Žigert Pleteršek, Petra, 2022. "Szeged-like entropies of graphs," Applied Mathematics and Computation, Elsevier, vol. 431(C).
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