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On Sombor index of trees

Author

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  • Das, Kinkar Chandra
  • Gutman, Ivan

Abstract

This paper is concerned with the recently introduced Sombor index SO, defined asSO=SO(G)=∑vkvℓ∈E(G)dG(vk)2+dG(vℓ)2,where dG(v) is the degree of the vertex v of a graph G. We present bounds on SO of trees in terms of order, independence number, and number of pendent vertices, and characterize the extremal cases. In addition, analogous results for quasi-trees are established.

Suggested Citation

  • Das, Kinkar Chandra & Gutman, Ivan, 2022. "On Sombor index of trees," Applied Mathematics and Computation, Elsevier, vol. 412(C).
    • Handle: RePEc:eee:apmaco:v:412:y:2022:i:c:s0096300321006597
    DOI: 10.1016/j.amc.2021.126575
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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. Lkhagva Buyantogtokh & Batmend Horoldagva & Kinkar Chandra Das, 2020. "On reduced second Zagreb index," Journal of Combinatorial Optimization, Springer, vol. 39(3), pages 776-791, April.
    3. Kinkar Chandra Das & Yilun Shang, 2021. "Some Extremal Graphs with Respect to Sombor Index," Mathematics, MDPI, vol. 9(11), pages 1-15, May.
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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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