Line cozero-divisor graphs

Abstract

Let R be a commutative ring. The cozero-divisor graph of R denoted by Γ′(R) is a graph with the vertex set W∗(R), where W∗(R) is the set of all non-zero and non-unit elements of R, and two distinct vertices x and y are adjacent if and only if x ∈/ Ry and y ∈/ Rx. In this paper, we investigate when the cozero-divisor graph is a line graph. We completely present all commutative rings which their cozero-divisor graphs are line graphs. Also, we study when the cozero-divisor graph is the complement of a line graph