An ideal-based cozero-divisor graph of a commutative ring

TL;DR

This paper introduces a new graph structure called the cozero-divisor graph for commutative rings with respect to an ideal, exploring its properties and related results.

Contribution

The paper defines the cozero-divisor graph of a ring relative to an ideal and investigates its properties, providing new insights into ring and graph theory connections.

Findings

Defined the cozero-divisor graph $ ilde{ ext{Gamma}}_I(R)$ for a commutative ring and ideal.

Derived properties and structural results of the cozero-divisor graph.

Established relationships between ring-theoretic concepts and graph-theoretic properties.

Abstract

Let $R$ be a commutative ring and let $I$ be an ideal of $R$. In this paper, we introduce the cozero-divisor graph $\acute{\Gamma}_I(R)$ of $R$ and obtain some related results.