  Assume that $R$ is a commutative ring with nonzero identity. In this paper,
we introduce and investigate zero-annihilator graph of $R$ denoted by
$\mathtt{ZA}(R)$. It is the graph whose vertex set is the set of all nonzero
nonunit elements of $R$ and two distinct vertices $x$ and $y$ are adjacent
whenever ${\rm Ann}_R(x)\cap {\rm Ann}_R(y)=\{0\}$.
