Nil Clean Divisor Graph

Abstract

In this article, we introduce a new graph theoretic structure associated with a finite commutative ring, called nil clean divisor graph. For a ring $R$, nil clean divisor graph is denoted by $G_N(R)$, where the vertex set is $\{x\in R\,:\, x\neq 0, \,\exists\, y(\neq 0, \neq x)\in R$ such that $xy$ is nil clean$\}$, two vertices $x$ and $y$ are adjacent if $xy$ is a nil clean element. We prove some interesting results of nil clean divisor graph of a ring.