Abstract
Let R be a commutative ring with identity, and let Z(R) be the set of zero-divisors of R. The total graph of R is the graph T(?(R)) whose vertices are all elements of R, and two distinct vertices x and y are adjacent if and only if x + y ? Z(R). We investigate the perfectness of the graphs Z0(?(R)), T0(?(R)) and T(?(R)), where Z0(?(R)) and T0(?(R)) are (induced) subgraphs of T(?(R)) on Z(R)* = Z(R) \ {0} and R* = R \ {0}, respectively.
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