| Issue |
RAIRO-Oper. Res.
Volume 59, Number 5, September-October 2025
|
|
|---|---|---|
| Page(s) | 2615 - 2632 | |
| DOI | https://doi.org/10.1051/ro/2025084 | |
| Published online | 12 September 2025 | |
Extremal values of two multiplicative type topological indices
1
College of Mathematics Science, Inner Mongolia Minzu University, Tongliao 028000, P.R. China
2
Department of Mathematics, Sungkyunkwan University, Suwon 16419, Republic of Korea
3
School of Mathematical Sciences, Bohai University, Jinzhou 121013, P.R. China
* Corresponding author: kinkardas2003@gmail.com
Received:
18
November
2024
Accepted:
20
June
2025
The multiplicative-type topological index of a graph is defined as the product of a symmetric function of the degrees of all adjacent vertices. It can be regarded as the multiplicative version of the vertex-degree-based topological index of the graph. Based on some graph operations, the extremal values of the multiplicative sum Zagreb index for trees with at most three branch vertices are determined. Some upper bounds of the multiplicative sum Zagreb index in relation to graph parameters are also provided. Furthermore, the extremal values of the multiplicative Sombor index for chemical graphs and chemical trees are completely characterized, respectively.
Mathematics Subject Classification: 05C35 / 05C09 / 92E10 / 05C07
Key words: Extremal value / topological index / chromatic number / tree
© The authors. Published by EDP Sciences, ROADEF, SMAI 2025
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