As it was already known and can still be seen in literature that if R is a ring , then A clean element x of R is an element that can be written as a sum of an idempotent and a unit of R. A ring R is clean if all its elements are clean. A clean graph of a ring (Cl(R) ) is graph whose vertices are of the form (e, u) where e is an idempotent and u is a unit in R and two vertices (e, u) and (f, v) are connected if and only if either ef = 0 or uv = vu = 1. Please apart from structural visualization, what other application of Cl(R) do we have?
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