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Let $R$ be a finite commutative ring with nonzero identity and denote its
Jacobson radical by $J(R)$. The Jacobson graph of $R$ is the graph in which
the vertex set is $R\setminus J(R)$, and two distinct vertices $x$ and $y$
are adjacent if and only if $1-xy$ is not a unit in $R$. In this paper, the
nonorientable genus of some Jacobson graphs is either computed or estimated
by a lower bound. As an application, the rings $R$ with projective Jacobson
graphs are classified.
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