**Nasrin Dehgardi, Zhibin Du and Yilun Shang**

Notes on Number Theory and Discrete Mathematics

Print ISSN 1310–5132, Online ISSN 2367–8275

Volume 30, 2024, Number 2, Pages 453–460

DOI: 10.7546/nntdm.2024.30.2.453-460

**Full paper (PDF, 196 Kb)**

## Details

### Authors and affiliations

Nasrin Dehgardi

*Department of Mathematics and Computer Science, Sirjan University of Technology
Sirjan, Iran*

Zhibin Du

*School of Software, South China Normal University
Foshan, Guangdong 528225, China*

Yilun Shang

*Department of Computer and Information Sciences, Northumbria University
Newcastle NE1 8ST, United Kingdom*

### Abstract

For a graph , the multiplicative Sombor index is defined as

where is the degree of vertex . Liu [Liu, H. (2022). *Discrete Mathematics Letters*, 9, 80–85] showed that, when is a tree of order , . We improved this result and show that, if is a tree of order with maximum degree , then

Also, we show that equality holds if and only if is a spider whose all legs have length less than three or all legs have length more than one.

### Keywords

- Sombor index
- Multiplicative Sombor index
- Trees

### 2020 Mathematics Subject Classification

- 05C07

### References

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### Manuscript history

- Received: 17 October 2023
- Revised: 3 June 2024
- Accepted: 18 July 2024
- Online First: 20 July 2024

### Copyright information

Ⓒ 2024 by the Authors.

This is an Open Access paper distributed under the terms and conditions of the Creative Commons Attribution 4.0 International License (CC BY 4.0).

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## Cite this paper

Dehgardi, N., Du, Z., & Shang, Y. (2024). Multiplicative Sombor index of trees. *Notes on Number Theory and Discrete Mathematics*, 30(2), 453-460, DOI: 10.7546/nntdm.2024.30.2.453-460.