Classification of rings with unit graphs having domination number less than four

Abstract

Let $R$ be a finite commutative ring with nonzero identity. The unit graph of $R$ is the graph obtained by setting all the elements of $R$ to be the vertices and defining distinct vertices $x$ and $y$ to be adjacent if and only if $x+y$ is a unit element of $R$. In this paper, a classification of finite commutative rings with nonzero identity in which their unit graphs have domination number less than four is given.