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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.
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