A Note on a Line Graph of the Zero Divisor Graph of a Commutative Ring

Abstract

The rings considered in this article are commutative with identity $ 1 \neq 0 $. Recall that the zero divisor graph of a ring $ R $ is a simple undirected graph whose vertex set is the set of all nonzero zero divisors of the ring $ R $ and two distinct vertices $ x, y $ are adjacent in this graph if and only if $xy = 0$. In this article we studied the line graph of the zero divisor graph of a ring and we proved some results regarding the diameter of the line graph.