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Some Extremal Graphs with Respect to Sombor Index

Author

Listed:
  • Kinkar Chandra Das

    (Department of Mathematics, Sungkyunkwan University, Suwon 16419, Korea)

  • Yilun Shang

    (Department of Computer and Information Sciences, Northumbria University, Newcastle NE1 8ST, UK)

Abstract

Let G be a graph with set of vertices V ( G ) ( | V ( G ) | = n ) and edge set E ( G ) . Very recently, a new degree-based molecular structure descriptor, called Sombor index is denoted by S O ( G ) and is defined as S O = S O ( G ) = ∑ v i v j ∈ E ( G ) d G ( v i ) 2 + d G ( v j ) 2 , where d G ( v i ) is the degree of the vertex v i in G . In this paper we present some lower and upper bounds on the Sombor index of graph G in terms of graph parameters (clique number, chromatic number, number of pendant vertices, etc.) and characterize the extremal graphs.

Suggested Citation

  • Kinkar Chandra Das & Yilun Shang, 2021. "Some Extremal Graphs with Respect to Sombor Index," Mathematics, MDPI, vol. 9(11), pages 1-15, May.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:11:p:1202-:d:562137
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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.
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    Citations

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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).
    2. Shang, Yilun, 2022. "Sombor index and degree-related properties of simplicial networks," Applied Mathematics and Computation, Elsevier, vol. 419(C).
    3. 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).
    4. Das, Kinkar Chandra & Gutman, Ivan, 2022. "On Sombor index of trees," Applied Mathematics and Computation, Elsevier, vol. 412(C).

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