| Autor: |
J. A. Méndez-Bermúdez, José M. Rodríguez, José L. Sánchez, José M. Sigarreta |
| Jazyk: |
angličtina |
| Rok vydání: |
2022 |
| Předmět: |
|
| Zdroj: |
Mathematical Biosciences and Engineering, Vol 19, Iss 9, Pp 8908-8922 (2022) |
| Druh dokumentu: |
article |
| ISSN: |
1551-0018 |
| DOI: |
10.3934/mbe.2022413?viewType=HTML |
| Popis: |
The aim of this work is to obtain new inequalities for the variable symmetric division deg index $ SDD_\alpha(G) = \sum_{uv \in E(G)} (d_u^\alpha/d_v^\alpha+d_v^\alpha/d_u^\alpha) $, and to characterize graphs extremal with respect to them. Here, by $ uv $ we mean the edge of a graph $ G $ joining the vertices $ u $ and $ v $, and $ d_u $ denotes the degree of $ u $, and $ \alpha \in \mathbb{R} $. Some of these inequalities generalize and improve previous results for the symmetric division deg index. In addition, we computationally apply the $ SDD_\alpha(G) $ index on random graphs and we demonstrate that the ratio $ \langle SDD_\alpha(G) \rangle/n $ ($ n $ is the order of the graph) depends only on the average degree $ \langle d \rangle $. |
| Databáze: |
Directory of Open Access Journals |
| Externí odkaz: |
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