The n-total graph of a commutative ring
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arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909737676701696 |
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| author | AitElhadi, Djamila Badawi, Ayman |
| author_facet | AitElhadi, Djamila Badawi, Ayman |
| contents | Let $R$ be a commutative ring with $1\not = 0$, $Z(R)$ be the set of all zero-divisors of $R$, and $n \geq 1$. This paper introduces the $n$-total graph of a commutative ring $R$. The $n$-total graph of a commutative ring $R$, denoted by $n-T(R)$, is an undirected simple graph with vertex set $R$, such that two vertices $x, y$ in $R$ are connected by an edge if $x^n + y^n$ in $Z(R)$. Note that if $n =1$, then the $1$-total graph of $R$ is the total graph of $R$ in the sense of Anderson-Badawi's paper on the total graph of a commutative ring. In this paper, we study some graph properties and theoretical ring structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_11361 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The n-total graph of a commutative ring AitElhadi, Djamila Badawi, Ayman Commutative Algebra 13A15, 13B99, 05C99 Let $R$ be a commutative ring with $1\not = 0$, $Z(R)$ be the set of all zero-divisors of $R$, and $n \geq 1$. This paper introduces the $n$-total graph of a commutative ring $R$. The $n$-total graph of a commutative ring $R$, denoted by $n-T(R)$, is an undirected simple graph with vertex set $R$, such that two vertices $x, y$ in $R$ are connected by an edge if $x^n + y^n$ in $Z(R)$. Note that if $n =1$, then the $1$-total graph of $R$ is the total graph of $R$ in the sense of Anderson-Badawi's paper on the total graph of a commutative ring. In this paper, we study some graph properties and theoretical ring structure. |
| title | The n-total graph of a commutative ring |
| topic | Commutative Algebra 13A15, 13B99, 05C99 |
| url | https://arxiv.org/abs/2508.11361 |