The domination and total domination numbers of a zero-divisor graph are equal for every commutative ring except Z2 × D with D a domain, where they are 1 and 2.
and Stickles, J., Cut structures in zero-divisor graphs of commutative rings, J
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Domination and Total Domination Numbers in Zero-divisor Graphs of Commutative Rings
The domination and total domination numbers of a zero-divisor graph are equal for every commutative ring except Z2 × D with D a domain, where they are 1 and 2.