Some results on the ideal-based cozero-divisor graph of a commutative ring

TL;DR

This paper investigates the properties of the ideal-based cozero-divisor graph of a commutative ring, providing new insights into its structure and characteristics.

Contribution

It introduces and analyzes the ideal-based cozero-divisor graph, offering new results on its properties within commutative rings.

Findings

Characterization of the graph's connectivity

Conditions for the graph to be complete or bipartite

Relationships between ring ideals and graph properties

Abstract

Let R be a commutative ring with identity and I be an ideal of R. The cozero-divisor graph with respect to I, denoted by $\Gamma''_I(R)$, is the graph of R with vertices {x \in R -I :xR +I \not=R} and two distinct vertices $x$ and $y$ are adjacent if and only if $x \not \in yR+I$ and $y \not \in xR+I$.In this paper, we obtained some results on $\Gamma''_I(R)$.