Ideal-Based Quasi Cozero Divisor Graph of a Commutative Ring

چکیده مقاله

Let R be a commutative ring with identity and I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by Γ_I(R), is the graph whose vertices are the set {x ∈ R∖I |xy ∈ I for some y ∈ R∖I} with distinct vertices x and y are adjacent if and only if xy ∈ I. The cozero-divisor graph with respect to I, denoted by (Formula presented.), is the graph of R with vertices {x ∈ R∖I|xR + I ≠ R} and two distinct vertices x and y are adjacent if and only if x ∉ yR + I and y ∉ xR + I. In this paper, we introduced and investigated an undirected graph (Formula presented.) of R with vertices (Formula presented.) and two distinct vertices x and y are adjacent if and only if x ∉ yR + I and y ∉ xR + I. Copyright © 2025 Faranak Farshadifar. Journal of Mathematics published by John Wiley & Sons Ltd.