Extremal graphs of multiplicative sum Zagreb index

Chunlei Xu, Guanru Li, Yiming Lei and Junming Hu
Notes on Number Theory and Discrete Mathematics
Print ISSN 1310–5132, Online ISSN 2367–8275
Volume 32, 2026, Number 1, Pages 242–253
DOI: 10.7546/nntdm.2026.32.1.242-253
Full paper (PDF, 269 Kb)

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Authors and affiliations

Chunlei Xu
College of Mathematics Science, Inner Mongolia Minzu University
Tongliao 028000, P. R. China

Guanru Li
College of Mathematics Science, Inner Mongolia Minzu University
Tongliao 028000, P. R. China

Yiming Lei
College of Mathematical Sciences, Bohai University
Jinzhou 121013, P. R. China

Junming Hu
College of Mathematics Science, Inner Mongolia Minzu University
Tongliao 028000, P. R. China

Abstract

The multiplicative sum Zagreb index, regarded as the multiplicative version of the first Zagreb index, is defined as the product of the degree sum over all pairs of adjacent vertices. In this paper, we determine the extremal values of the multiplicative sum Zagreb index for three class of trees. Some bounds on the multiplicative sum Zagreb index are obtained, and the corresponding extremal graphs with these bounds are characterized.

Keywords

• Extremal value
• Extremal graph
• Tree
• Bound

2020 Mathematics Subject Classification

• 05C35
• 05C09
• 92E10

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Manuscript history

• Received: 5 November 2025
• Revised: 11 March 2026
• Accepted: 19 March 2026
• Online First: 22 March 2026

Copyright information

Ⓒ 2026 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).