Abstract
The present work aims to exploit the interplay between the algebraic properties of rings and the graph-theoretic structures of their associated graphs. Let [Formula: see text] be an associative (not necessarily commutative) ring. We focus on the domination number of the zero-divisor graph [Formula: see text], the compressed zero-divisor graph [Formula: see text] and the unit graph [Formula: see text]. We find some relations between the domination number of the zero-divisor graph and that of the compressed zero-divisor graph. Moreover, some relations between the domination number of [Formula: see text] and [Formula: see text], as well as the relations between the domination number of [Formula: see text] and [Formula: see text], are studied.
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