Bulletin of the
Korean Mathematical Society BKMS

In this paper, we study domination in the zero-divisor graph of a $\ast$-ring. We first determine the domination number, the total domination number, and the connected domination number for the zero-divisor graph of the product of two $\ast$-rings with componentwise involution. Then, we study domination in the zero-divisor graph of a Rickart $\ast$-ring and relate it with the clique of the zero-divisor graph of a Rickart $\ast$-ring.

Keywords: $\ast$-ring, Rickart $\ast$-ring, domination number, dominating set, zero-divisor graph

MSC numbers: 16W10, 05C69, 05C25

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