Extremal problems on the general Sombor index of a graph

Juan C. Hernández; José M. Rodríguez; O. Rosario; José M. Sigarreta; Juan C. Hernández; José M. Rodríguez; O. Rosario; José M. Sigarreta

doi:10.3934/math.2022464

AIMS Mathematics

2022, Volume 7, Issue 5: 8330-8343. doi: 10.3934/math.2022464

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Research article

Extremal problems on the general Sombor index of a graph

1.
Facultad de Matemáticas, Universidad Autónoma de Guerrero, Carlos E. Adame No.54 Col. Garita, 39650 Acalpulco Gro., Mexico
2.
Departamento de Matemáticas, Universidad Carlos III de Madrid, Avenida de la Universidad 30, 28911 Leganés, Madrid, Spain

Received: 29 September 2021 Revised: 04 February 2022 Accepted: 15 February 2022 Published: 28 February 2022
MSC : 05C09, 05C92

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.
- Sombor indices,
- variable indices,
- degree-based topological indices,
- inequalities
Citation: Juan C. Hernández, José M. Rodríguez, O. Rosario, José M. Sigarreta. Extremal problems on the general Sombor index of a graph[J]. AIMS Mathematics, 2022, 7(5): 8330-8343. doi: 10.3934/math.2022464

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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.

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