Ideal-based quasi zero divisor graph

Year 2021, Volume: 50 Issue: 6, 1658 - 1666, 14.12.2021

Ece Yetkin Çelikel , Angsuman Das , Cihat Abdioğlu

https://doi.org/10.15672/hujms.822702

Abstract

Let $R$ be a commutative ring with identity and $I$ a proper ideal of $R$. In this paper we introduce the ideal-based quasi zero divisor graph $Q\Gamma_{I}(R)$ of $R$ with respect to $I$ which is an undirected graph with vertex set $V=\{a\in R\backslash\sqrt{I}:$ $ab\in I$ for some $b\in R\backslash\sqrt{I}\}$ and two distinct vertices $a$ and $b$ are adjacent if and only if $ab\in I$. We study the basic properties of this graph such as diameter, girth, dominaton number, etc. We also investigate the interplay between the ring theoretic properties of a Noetherian multiplication ring $R$ and the graph-theoretic properties of $Q\Gamma_{I}(R)$.

Keywords

Ideal-based zero divisor graph, quasi primary ideal, zero-divisor graph

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