Domination Parameters of Unit Graphs of Rings

Let R be a finite commutative ring with nonzero identity 1. In this paper, domination parameters, the domination number and the total dominating number, of the unit graph G(R) or the closed unit graph G¯(R) of R are investigated. To study the domination number of G(R), we prove that it suffices to consider the case when R is a direct product of fields. Furthermore, we discuss the domination number and total dominating number of the unit graph of the ring of integers modulo n.