On the domination and signed domination numbers of zero-divisor graph - Ebrahim Vatandoost; Fatemeh Ramezani (GTA Research Group, Univ. Newcastle, Indonesian Combinatorics Society and ITB, 2016)
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 brace and for distinct x,y 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 Z^*(R), x^2 ≠ 0. We characterize Γ(R) whose γ(Γ(R))+γ(Γ(R)) n+1,n,n-1 brace, where |Z^*(R)|=n.