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Open problems on Sombor index of unicyclic and bicyclic graphs

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  • Das, Kinkar Chandra

Abstract

Let Γ=(V,E) be a graph of order p. Recently, the Sombor index is introduced, defined asSO(Γ)=∑vivj∈E(Γ)dΓ(vi)2+dΓ(vj)2, where dΓ(vi) is the degree of the vertex vi in Γ. Cruz and Rada [4] obtained an upper bound on the Sombor index of unicyclic and bicyclic graphs of order p, but did not characterize the extremal graphs. In the same paper, they mentioned that the maximal graphs over the set of unicyclic and bicyclic graphs with respect to Sombor index, is an interesting problem that remains open. In this paper we completely solve these problems.

Suggested Citation

  • Das, Kinkar Chandra, 2024. "Open problems on Sombor index of unicyclic and bicyclic graphs," Applied Mathematics and Computation, Elsevier, vol. 473(C).
    • Handle: RePEc:eee:apmaco:v:473:y:2024:i:c:s009630032400119x
    DOI: 10.1016/j.amc.2024.128647
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    References listed on IDEAS

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    1. Das, Kinkar Chandra & Gutman, Ivan, 2022. "On Sombor index of trees," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    2. Cruz, Roberto & Gutman, Ivan & Rada, Juan, 2021. "Sombor index of chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    3. Rada, Juan & Rodríguez, José M. & Sigarreta, José M., 2023. "On integral Sombor indices," Applied Mathematics and Computation, Elsevier, vol. 452(C).
    4. Chen, Meng & Zhu, Yan, 2024. "Extremal unicyclic graphs of Sombor index," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    5. 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).
    6. Kinkar Chandra Das & Yilun Shang, 2021. "Some Extremal Graphs with Respect to Sombor Index," Mathematics, MDPI, vol. 9(11), pages 1-15, May.
    Full references (including those not matched with items on IDEAS)

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