On the Sombor index of the total graph and the unit graph of commutative rings
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arXiv
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| Hauptverfasser: | , , |
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| Format: | Preprint |
| Veröffentlicht: |
2024
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| _version_ | 1866909200411525120 |
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| author | Pathak, Abhishek Vaibhav Sachan, Anukul DSouza, Raisa |
| author_facet | Pathak, Abhishek Vaibhav Sachan, Anukul DSouza, Raisa |
| contents | In this paper, we investigate the Sombor index of the total graph and unit graph of $\mathbb{Z}_n$ which is denoted by $T_Γ(\mathbb{Z}_n)$ and $G(\mathbb{Z}_n)$ respectively for $n \in \{2k, p^α, pq, p^2q\}$ where $p$ and $q$ are distinct odd prime numbers such that $p < q$. Moreover, we compute the Sombor index of any finite local ring. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_07181 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the Sombor index of the total graph and the unit graph of commutative rings Pathak, Abhishek Vaibhav Sachan, Anukul DSouza, Raisa Combinatorics 05C50 In this paper, we investigate the Sombor index of the total graph and unit graph of $\mathbb{Z}_n$ which is denoted by $T_Γ(\mathbb{Z}_n)$ and $G(\mathbb{Z}_n)$ respectively for $n \in \{2k, p^α, pq, p^2q\}$ where $p$ and $q$ are distinct odd prime numbers such that $p < q$. Moreover, we compute the Sombor index of any finite local ring. |
| title | On the Sombor index of the total graph and the unit graph of commutative rings |
| topic | Combinatorics 05C50 |
| url | https://arxiv.org/abs/2405.07181 |