Ideal‐Based Quasi Cozero Divisor Graph of a Commutative Ring

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 | x y ∈ I for some y ∈ R ∖ I } with distinct vertices x and y are adjacent if and only if x y ∈ I . The cozero‐divisor graph with respect to I , denoted by , is the graph of R with vertices { x ∈ R ∖ I | x R + I ≠ R } and two distinct vertices x and y are adjacent if and only if x ∉ y R + I and y ∉ x R + I . In this paper, we introduced and investigated an undirected graph of R with vertices and two distinct vertices x and y are adjacent if and only if x ∉ y R + I and y ∉ x R + I .