On a new extension of the zero-divisor graph

A. Cherrabi; H. Essannouni; E. Jabbouri; A. Ouadfel

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arXiv · 1806.11442

On a new extension of the zero-divisor graph

A. Cherrabi·H. Essannouni·E. Jabbouri·A. Ouadfel

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Abstract

In this paper, we introduce a new graph whose vertices are the nonzero zero-divisors of commutative ring $R$ and for distincts elements $x$ and $y$ in the set $Z(R)^{\star}$ of the nonzero zero-divisors of $R$, $x$ and $y$ are adjacent if and only if $xy=0$ or $x+y\in Z(R)$. we present some properties and examples of this graph and we study his relation with the zero-divisor graph and with a subgraph of total graph of a commutative ring.

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BibTeX RIS

A. Cherrabi, H. Essannouni, E. Jabbouri, A. Ouadfel. 2018-06-28. On a new extension of the zero-divisor graph. https://arxiv.org/abs/1806.11442

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