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More on Sombor Index of Graphs

Author

Listed:
  • Wenjie Ning

    (College of Science, China University of Petroleum (East China), Qingdao 266580, China)

  • Yuheng Song

    (College of Science, China University of Petroleum (East China), Qingdao 266580, China)

  • Kun Wang

    (College of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, China)

Abstract

Recently, a novel degree-based molecular structure descriptor, called Sombor index was introduced. Let G = ( V ( G ) , E ( G ) ) be a graph. Then, the Sombor index of G is defined as S O ( G ) = ∑ u v ∈ E ( G ) d G 2 ( u ) + d G 2 ( v ) . In this paper, we give some lemmas that can be used to compare the Sombor indices between two graphs. With these lemmas, we determine the graph with maximum S O among all cacti with n vertices and k cut edges. Furthermore, the unique graph with maximum S O among all cacti with n vertices and p pendant vertices is characterized. In addition, we find the extremal graphs with respect to S O among all quasi-unicyclic graphs.

Suggested Citation

  • Wenjie Ning & Yuheng Song & Kun Wang, 2022. "More on Sombor Index of Graphs," Mathematics, MDPI, vol. 10(3), pages 1-12, January.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:3:p:301-:d:728097
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    References listed on IDEAS

    as
    1. Das, Kinkar Ch. & Gutman, Ivan & Nadjafi–Arani, Mohammad J., 2015. "Relations between distance–based and degree–based topological indices," Applied Mathematics and Computation, Elsevier, vol. 270(C), pages 142-147.
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