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Sombor index of chemical graphs

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  • Cruz, Roberto
  • Gutman, Ivan
  • Rada, Juan

Abstract

A graph G consists of a set of vertices V(G) and a set of edges E(G). Recently, a new vertex-degree-based molecular structure descriptor was introduced, defined asSO(G)=∑uv∈E(G)(du)2+(dv)2and named “Sombor index”. By du is denoted the degree of the vertex u∈V(G). In this paper we are concerned with the Sombor index of chemical graphs. Recall that G is a chemical graph if du≤4 for all u∈V(G). We characterize the graphs extremal with respect to the Sombor index over the following sets: (connected) chemical graphs, chemical trees, and hexagonal systems.

Suggested Citation

  • Cruz, Roberto & Gutman, Ivan & Rada, Juan, 2021. "Sombor index of chemical graphs," Applied Mathematics and Computation, Elsevier, vol. 399(C).
    • Handle: RePEc:eee:apmaco:v:399:y:2021:i:c:s0096300321000667
    DOI: 10.1016/j.amc.2021.126018
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    References listed on IDEAS

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    1. Cruz, Roberto & Monsalve, Juan & Rada, Juan, 2020. "Extremal values of vertex-degree-based topological indices of chemical trees," Applied Mathematics and Computation, Elsevier, vol. 380(C).
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    Cited by:

    1. Cruz, Roberto & Rada, Juan & Sigarreta, José M., 2021. "Sombor index of trees with at most three branch vertices," Applied Mathematics and Computation, Elsevier, vol. 409(C).
    2. Zhang, Weilin & You, Lihua & Liu, Hechao & Huang, Yufei, 2021. "The expected values and variances for Sombor indices in a general random chain," Applied Mathematics and Computation, Elsevier, vol. 411(C).
    3. Kinkar Chandra Das & Yilun Shang, 2021. "Some Extremal Graphs with Respect to Sombor Index," Mathematics, MDPI, vol. 9(11), pages 1-15, May.
    4. Sun, Xiaoling & Du, Jianwei, 2022. "On Sombor index of trees with fixed domination number," Applied Mathematics and Computation, Elsevier, vol. 421(C).
    5. 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).
    6. Chen, Meng & Zhu, Yan, 2024. "Extremal unicyclic graphs of Sombor index," Applied Mathematics and Computation, Elsevier, vol. 463(C).
    7. Das, Kinkar Chandra & Gutman, Ivan, 2022. "On Sombor index of trees," Applied Mathematics and Computation, Elsevier, vol. 412(C).

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    1. 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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