The $n$-total graph of an integral domain
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866911378904711168 |
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| author | AbiHabib, Myriam Badawi, Ayman |
| author_facet | AbiHabib, Myriam Badawi, Ayman |
| contents | Let $R$ be a finite product of integral domains and $D$ be a union of prime ideals (it is possible that $R$ is just an integral domain). Let $n \geq 1$ be a positive integer. This paper introduces the $n$-total graph of a $(R, D)$. The $n$-total graph of $(R, D)$, 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 $x^n + y^n \in D$. In this paper, we study some graph properties and theoretical ring structure. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2601_10845 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | The $n$-total graph of an integral domain AbiHabib, Myriam Badawi, Ayman Commutative Algebra 13A15, 3B99, 05C99 Let $R$ be a finite product of integral domains and $D$ be a union of prime ideals (it is possible that $R$ is just an integral domain). Let $n \geq 1$ be a positive integer. This paper introduces the $n$-total graph of a $(R, D)$. The $n$-total graph of $(R, D)$, 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 $x^n + y^n \in D$. In this paper, we study some graph properties and theoretical ring structure. |
| title | The $n$-total graph of an integral domain |
| topic | Commutative Algebra 13A15, 3B99, 05C99 |
| url | https://arxiv.org/abs/2601.10845 |