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The unit graph of a ring $R$ with nonzero identity is the graph in which
the vertex set is $R$, and two distinct vertices $x$ and $y$ are adjacent
if and only if $x+y$ is a unit in $R$. In this paper, we derive several
necessary conditions for the nonplanarity of the unit graphs of finite
commutative rings with nonzero identity, and determine, up to isomorphism,
all finite commutative rings with nonzero identity whose unit graphs are
toroidal.
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