The cozero-divisor graph of a module

Abstract

Let [Formula: see text] be an associative ring with non-zero identity and [Formula: see text] a non-zero unital left [Formula: see text]-module. The cozero-divisor graph of [Formula: see text], denoted by [Formula: see text], is a graph with vertices [Formula: see text] and two distinct vertices [Formula: see text] and [Formula: see text] are adjacent if [Formula: see text] and [Formula: see text]. In this paper, we study some connections between the graph-theoretic properties of [Formula: see text] and algebraic-theoretic properties of [Formula: see text] and [Formula: see text]. Also, we study girth, independence number, clique number and planarity of this graph.