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 ΓI(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 ΓI″R, 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 QΓI″R of R with vertices x∈R∖IxR+I≠R and xR+I=xR+I and two distinct vertices x and y are adjacent if and only if x ∉ yR + I and y ∉ xR + I.