On the domination and signed domination numbers of zero-divisor graph

Let R be a commutative ring (with 1) and let Z(R) be its set of zero-divisors. The zero-divisor graph Γ (R) has vertex set Z*(R) = Z(R) │ {0} and for distinct x; y є Z*(R), the vertices x and y are adjacent if and only if xy = 0. In this paper, we consider the domination number and signed domination number on zero-divisor graph Γ (R) of commutative ring R such that for every 0 ≠ x є Z*(R), x^2 ≠ 0. We characterize Γ(R) whose y(Γ(R)) + y((ΓR)) є {n + 1; n; n - 1}, where │Z*(R)│ = n.