| Autor: |
Qiaozhi Geng, Shengjie He, Rong-Xia Hao |
| Jazyk: |
angličtina |
| Rok vydání: |
2023 |
| Předmět: |
|
| Zdroj: |
AIMS Mathematics, Vol 8, Iss 12, Pp 30059-30074 (2023) |
| Druh dokumentu: |
article |
| ISSN: |
2473-6988 |
| DOI: |
10.3934/math.20231537?viewType=HTML |
| Popis: |
Let $ H $ be a graph with edge set $ E_H $. The Sombor index and the reduced Sombor index of a graph $ H $ are defined as $ SO(H) = \sum\limits_{uv\in E_H}\sqrt{d_{H}(u)^{2}+d_{H}(v)^{2}} $ and $ SO_{red}(H) = \sum\limits_{uv\in E_H}\sqrt{(d_{H}(u)-1)^{2}+(d_{H}(v)-1)^{2}} $, respectively. Where $ d_{H}(u) $ and $ d_{H}(v) $ are the degrees of the vertices $ u $ and $ v $ in $ H $, respectively. A cactus is a connected graph in which any two cycles have at most one common vertex. Let $ \mathcal{C}(n, k) $ be the class of cacti of order $ n $ with $ k $ cycles. In this paper, the lower bound for the Sombor index of the cacti in $ \mathcal{C}(n, k) $ is obtained and the corresponding extremal cacti are characterized when $ n\geq 4k-2 $ and $ k\geq 2 $. Moreover, the lower bound of the reduced Sombor index of cacti is obtained by similar approach. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
|
