This paper aims to find certain bounds for the domination number of Latin square graphs, i.e., a simple graph assigned to a Latin square. In fact, we show that if [Formula: see text] is a Latin square of order [Formula: see text] and [Formula: see text] is the associated Latin square graph of [Formula: see text], then [Formula: see text]. We will investigate in which case the equalities hold. Finally, we study the domination number of Latin square graph associated to groups. In particular, we show that if [Formula: see text], then [Formula: see text]. Also, we prove that if [Formula: see text], then [Formula: see text].

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A Latin square graph [Formula: see text] is a simple graph associated with a Latin square [Formula: see text]. In this paper, we consider a Latin square graph [Formula: see text] in which [Formula: see text] and improve the upper bound of the domination number [Formula: see text] by showing that [Formula: see text]. Moreover, we study certain domination numbers like medium domination, accurate domination, independent transversal domination and vertex covering transversal domination for Latin square graphs of order [Formula: see text] to give useful facts.

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