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Research Article | Open Access

Extremal problems on the general Sombor index of a graph

Juan C. Hernández1, José M. Rodríguez2, O. Rosario1, José M. Sigarreta1( )
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain
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Abstract

In this work we obtain new lower and upper optimal bounds of general Sombor indices. Specifically, we get inequalities for these indices relating them with other indices: the first Zagreb index, the forgotten index and the first variable Zagreb index. Finally, we solve some extremal problems for general Sombor indices.

Keywords

Sombor indicesvariable indicesdegree-based topological indicesinequalities
CLC number: 05C09, 05C92

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AIMS Mathematics
Volume 7 Issue 5,
May 2022
Pages 8330-8343
DOI: 10.3934/math.2022464

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Hernández JC, Rodríguez JM, Rosario O, et al. Extremal problems on the general Sombor index of a graph. AIMS Mathematics, 2022, 7(5): 8330-8343. https://doi.org/10.3934/math.2022464

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Received: 29 September 2021
Revised: 04 February 2022
Accepted: 15 February 2022
Published: 15 May 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)