Maximum values of the Sombor-index-like graph invariants of trees and connected graphs
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2023
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| _version_ | 1866916196885987328 |
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| author | Bašić, Milan |
| author_facet | Bašić, Milan |
| contents | A set of novel vertex-degree-based invariants was introduced by Gutman, denoted by \newline $SO_1, SO_2, \ldots,SO_6$. These invariants were constructed through geometric reasoning based on a new graph invariant framework. Motivated by proposed open problems in [Z. Tang, Q. Li, H. Deng, \textit{Trees with Extremal Values of the Sombor-Index-Like Graph Invariants}, MATCH Commun. Math. Comput. Chem. \textbf{90} (2023) 203-222], we have found the maximum values of $SO_5$ and $SO_6$ in the set of molecular trees with a given number of vertices, respectively, and we have found the maximum value of $SO_5$ in a class of connected graphs. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_02925 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Maximum values of the Sombor-index-like graph invariants of trees and connected graphs Bašić, Milan Discrete Mathematics Combinatorics 05C09, 11A07, 26C15, 26C10 A set of novel vertex-degree-based invariants was introduced by Gutman, denoted by \newline $SO_1, SO_2, \ldots,SO_6$. These invariants were constructed through geometric reasoning based on a new graph invariant framework. Motivated by proposed open problems in [Z. Tang, Q. Li, H. Deng, \textit{Trees with Extremal Values of the Sombor-Index-Like Graph Invariants}, MATCH Commun. Math. Comput. Chem. \textbf{90} (2023) 203-222], we have found the maximum values of $SO_5$ and $SO_6$ in the set of molecular trees with a given number of vertices, respectively, and we have found the maximum value of $SO_5$ in a class of connected graphs. |
| title | Maximum values of the Sombor-index-like graph invariants of trees and connected graphs |
| topic | Discrete Mathematics Combinatorics 05C09, 11A07, 26C15, 26C10 |
| url | https://arxiv.org/abs/2305.02925 |