Some results on the ideal-based cozero-divisor graph of a commutative ring

Abstract

Let R be a commutative ring with identity and I be an ideal of R. The cozero-divisor graph with respect to I, denoted by ${\Gamma }_I^{\prime \prime }(R)$, is the graph of R with vertices {x \in R -I :xR +I \not=R} and two distinct vertices $x$ and $y$ are adjacent if and only if $x\notin yR+I$ and $y\notin xR+I$.In this paper, we obtained some results on ${\Gamma }_I^{\prime \prime }(R)$.