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Let $R$ be a ring with nonzero identity. The unit graph of $R$,
denoted by $G(R)$, has its set of vertices equal to the set of all elements
of $R$; distinct vertices $x$ and $y$ are adjacent if and only if
$x+y$ is a unit of $R$. In this article, the basic properties of $G(R)$ are
investigated and some characterization results regarding connectedness,
chromatic index, diameter, girth, and planarity of $G(R)$ are given.
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