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arXiv · 2405.07181

On the Sombor index of the total graph and the unit graph of commutative rings

Abhishek Vaibhav Pathak·Anukul Sachan·Raisa DSouza
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Abstract

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.

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Abhishek Vaibhav Pathak, Anukul Sachan, Raisa DSouza. 2024-05-12. On the Sombor index of the total graph and the unit graph of commutative rings. https://arxiv.org/abs/2405.07181

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