“School of Mathematics”
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Paper IPM / M / 11142  


Abstract:  
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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