| Autor: |
Guifu Su, Yue Wu, Xiaowen Qin, Junfeng Du, Weili Guo, Zhenghang Zhang, Lifei Song |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 8, Iss 12, Pp 29352-29367 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231502?viewType=HTML |
| Popis: |
The cyclomatic number, denoted by $ \gamma $, of a graph $ G $ is the minimum number of edges of $ G $ whose removal makes $ G $ acyclic. Let $ \mathscr{G}_{n}^{\gamma} $ be the class of all connected graphs with order $ n $ and cyclomatic number $ \gamma $. In this paper, we characterized the graphs in $ \mathscr{G}_{n}^{\gamma} $ with minimum general Randić index for $ \gamma\geq 3 $ and $ 1\leq\alpha\leq \frac{39}{25} $. These extend the main result proved by A. Ali, K. C. Das and S. Akhter in 2022. The elements of $ \mathscr{G}_{n}^{\gamma} $ with maximum general Randić index were also completely determined for $ \gamma\geq 3 $ and $ \alpha\geq 1 $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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