On zero-divisor graph of the ring of Gaussian integers modulo $2^n$
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arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915225624641536 |
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| author | Venkatesan, Aruna Paramasivam, Krishnan K, M. Sabeel |
| author_facet | Venkatesan, Aruna Paramasivam, Krishnan K, M. Sabeel |
| contents | For a commutative ring $R$, the zero-divisor graph of $R$ is a simple graph with the vertex set as the set of all zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. This article attempts to predict the structure of the zero-divisor graph of the ring of Gaussian integers modulo $2$ to the power $n$ and determine the size, chromatic number, clique number, independence number, and matching through associate classes of divisors of $2^n$ in $\mathbb{Z}_{2^n}[i]$. In addition, a few topological indices of the corresponding zero-divisor graph, are obtained. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_02493 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On zero-divisor graph of the ring of Gaussian integers modulo $2^n$ Venkatesan, Aruna Paramasivam, Krishnan K, M. Sabeel Commutative Algebra Combinatorics Number Theory 05C78, 05C25, 05E40, 05C09 For a commutative ring $R$, the zero-divisor graph of $R$ is a simple graph with the vertex set as the set of all zero-divisors of $R$ and two distinct vertices $x$ and $y$ are adjacent if and only if $xy = 0$. This article attempts to predict the structure of the zero-divisor graph of the ring of Gaussian integers modulo $2$ to the power $n$ and determine the size, chromatic number, clique number, independence number, and matching through associate classes of divisors of $2^n$ in $\mathbb{Z}_{2^n}[i]$. In addition, a few topological indices of the corresponding zero-divisor graph, are obtained. |
| title | On zero-divisor graph of the ring of Gaussian integers modulo $2^n$ |
| topic | Commutative Algebra Combinatorics Number Theory 05C78, 05C25, 05E40, 05C09 |
| url | https://arxiv.org/abs/2504.02493 |