Nil clean graph of rings

Abstract

In this article, we have defined nil clean graph of a ring $R$. The vertex set is the ring $R$, two ring elements $a$ and $b$ are adjacent if and only if $a+b$ is nil clean in $R$. Graph theoretic properties like girth, dominating set, diameter etc. of nil clean graph have been studied for finite commutative rings.

15 pages, 8 figures