Ideal-based quasi cozero divisor graph of a commutative ring

Let R be a commutative ring with identity, and let I be an ideal of R. The zero-divisor graph of R with respect to I, denoted by I (R), is the graph whose vertices are the set \x R I | xy I for some y R I\, where distinct vertices x and y are adjacent if and only if xy I. The cozero-divisor graph with respect to I, denoted by ''I (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 introduce and investigate an undirected graph Q''I (R) of R with vertices \x R I | xR + 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.