Some results on the domination number of a zero-divisor graph

Abstract

In this paper, we investigate the domination, total domination, and semi-total domination numbers of a zero-divisor graph of a commutative Noetherian ring. Also, some relations between the domination numbers of Γ(R/I) and ΓI (R), and the domination numbers of Γ(R) and Γ(R[x[α δ]), where R[x, α, δ] is the Ore extension of R, are studied.