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 Gamma(R) has vertex set Z* (R) = Z (R) \ {0} and for distinct x; y is an element of 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 Gamma(R) of commutative ring R such that for every 0 not equal x is an element of Z* (R), x(2) not equal 0. We characterize Gamma(R) whose gamma(Gamma(R)) + gamma(<(Gamma(R))over bar>) is an element of {n + 1; n; n - 1}, where vertical bar Z* (R) vertical bar = n.