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Extremal unicyclic graphs of Sombor index

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Listed:
  • Chen, Meng
  • Zhu, Yan

Abstract

Unicyclic graph is one kind of typical graph for indices basing degree of vertex. Various chemical structures can be exhibited in unicyclic graph as well. A graph is said to be unicyclic if the graph is connected and |V(G)|=|E(G)|. Recently, the Sombor index, which is defined bySO=SO(G)=∑uv∈E(G)dG2(u)+dG2(v), was proposed by Gutman. This paper establishes distinct bounds for this index of unicyclic graph with girth l, as well as specific bounds of chemical unicyclic graph with girth l.

Suggested Citation

  • Chen, Meng & Zhu, Yan, 2024. "Extremal unicyclic graphs of Sombor index," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    • Handle: RePEc:eee:apmaco:v:463:y:2024:i:c:s009630032300543x
    DOI: 10.1016/j.amc.2023.128374
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    References listed on IDEAS

    as
    1. Cruz, Roberto & Gutman, Ivan & Rada, Juan, 2021. "Sombor index of chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    2. 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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    Cited by:

    1. Rada, Juan & Rodríguez, José M. & Sigarreta, José M., 2024. "Sombor index and elliptic Sombor index of benzenoid systems," Applied Mathematics and Computation, Elsevier, vol. 475(C).
    2. 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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