Ideal-based quasi zero divisor graph

Authors : Ece YETKİN ÇELİKEL, Angsuman DAS, Cihat ABDİOĞLU

Pages : 1658-1666

Doi:10.15672/hujms.822702

View : 16 | Download : 6

Publication Date : 2021-12-14

Article Type : Research Paper

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 $Q\Gamma_{I}insert ignore into journalissuearticles values(R);$ 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 $Q\Gamma_{I}insert ignore into journalissuearticles values(R);$.
Keywords : Ideal based zero divisor graph, quasi primary ideal, zero divisor graph